In the ocean of Europa in our own solar system :).
NASA's sending a probe to Jupiter's moon Europa. It might be home to life. (The geysers here are speculative - known to exist for Enceladus, indirect evidence so far though for Europa as we haven't been able to study it so thoroughly close up and its geysers also if they exist are harder to spot and may be sporadic).
A civilization that develops in a subsurface ocean would probably not have technology at least not at an advanced level, without fire. And how would they develop fire in an ocean? They would have hydrothermal vents, even lava at times possibly - but what's the chance of developing technology like ours? And even more so if they are like dolphins and don't have hands.
But they could have language, mathematics, art, music, etc etc, could be a billion years old high level of civilization even well beyond us, and we wouldn't know about them (because we can't see through the ice yet with our technology) and they wouldn't know about us.
EUROPAN LIFE AND OXYGEN
I say Europa as perhaps the best candidate of the possible subsurface icy moon oceans, because it probably is an oxygen rich ocean, oxygen created in the surface by radiation from Jupiter breaking apart water in the ice, then circulated into its ocean. And oxygen rich ocean + hydrothermal vents seems to suggest possibility of higher life with high energy requirements.
The rate of supply of oxygen is low compared to Earth with photosynthetic life. But if it is like hydrothermal vent communities in a large ocean, it's a mix of H2S and methane breathing and oxygen based life. So the aerobes could be surviving on food from non aerobes. And also just locally numerous - there might be only a small carrying capacity for the entire ocean, and still, have plenty of oxygen for complex life around every single hydrothermal vent in its oceans.
That's not enough for a civilization of 7 billion humans obviously, but if you think of more like the early hunter gatherer type stage of humans, no reason why it couldn't have a small population civilization. Or if the beings are small.
Gray parrots are very intelligent and weigh about half a kilogram each.Average weight of common parrot species. So could easily have a few million of some species that weighs that amount, and still have plenty of kilograms for the rest of their megafauna.
COULD AS EASILY BE AHEAD AS BEHIND US EVOLUTIONARILY
And the thing is, highly unlikely their evolution has developed in lock step with Earth.
If they could potentially have evolved as far as animals, e.g. fish or squid like creatures, as many seem to think is at least remotely possible - they could as easily be a half billion years ahead of us in evolution, as behind us, over a timescale of 4.7 billion years. We could find life there that is equivalent of what might evolve on Earth half a billion years from now in complexity of the life.
So not just intelligent life, it could also be more complex more highly evolved life than us. For instance, if there is some future stage for instance, after multi-cellularity - it might have evolved already on Europa - as multicellularity in its modern form developed only half a billion or so years ago on Earth.
Not saying that is probable. We have nowhere near enough understanding anyway to assign probability levels to such things. But seems not impossible, and you only asked "could", not "probable" :).
TIDALLY HEATED OCEANS ELSEWHERE IN OUR SOLAR SYSTEM - OORT CLOUD
And given this possibility of life in oceans of icy moons, well tidally heated oceans could exist anywhere even in furthest reaches of the Oort cloud. If you have systems of moons there and they are not tidally locked, or have radiation heat sources, or long lived ocean after a major impact - well - life could potentially evolve.
There could be thousands of "subsurface ocean" moons in the Oort cloud, as active or more active than Pluto and Charon. maybe never reached tidal locking. By probability are likely to be worlds there that are significantly larger than Pluto. Maybe Mars or Earth sized, and remote possibility perhaps, even Neptune sized.
Though Europa may seem the best bet at present for intelligence, we have no idea really what is out in the Oort cloud. Maybe it has thousands of ocean worlds covered in ice.
If there were any reason to suppose that any of them could have enough energy for complex life, then the sheer number of worlds and huge total volume of liquid water could make that more favourable, even if the probability was much less than for Europa that any individual one of them has a civilization.
If it turns out that any of them have sufficient energy sources for complex life, and that some of them do have complex lifeforms, our descendants may have to do a long search before they can be sure whether or not there is no civilization in any of those oceans.
TITAN'S METHANE OCEANS AND OTHER EXOTIC BIOCHEMISTRIES
Of course that is a rather Earth - centric way of looking at it. Could be other forms of higher life in our solar system also, conceivably, e.g. in the seas of Titan, we wouldn't know about them yet either, radically different biology if they exist. And again at those low temperatures, hard to see how they could develop fire or technology, supposing there was an ancient civilization there. Without technology then again could be hard to spot. According to Dirk Schulze-Makuch's book on places for life in the solar system, the conditions on Titan apparently don't seem very favourable for a complex ecosystem but it can't be ruled out. For this and other ideas of alternative biologies in our solar system, see Cosmic Biology.
There are also other newer ideas including life in supercritical CO2. Even in our own oceans. At the high pressures of the ocean depths, anywhere below around 0.8 kilometers depth, CO2 is a liquid. See "Life in liquid carbon dioxide". The first discovery of natural liquid CO2 in the oceans goes back to 1990. Interestingly, as you raise its temperature, liquid CO2 at around 31.1 C and 73.8 atmospheres in pressure becomes supercritical. That's a phase where the distinction between a gas and a liquid disappears and the properties often change. Liquid CO2 is often used for sterilizing. However, some microbes and their enzymes can tolerate living in liquid CO2. This was a surprising recent discovery reported in February of this year. They found six strains of microbes, isolated from three sites targeted for geological carbon dioxide sequestration - that have the astonishing ability to grow on the interface between water and supercritical CO2. See Microbial growth under supercritical CO2.
There are fairly large reservoirs of liquid CO2 beneath the Earth's oceans. For instance a CO2 lake found off the coast of Taiwan at a depth of 1.4 kilometers. It is heavier than water below a depth of around 3,000 km, so there may be extensive deeper reservoirs. It is a bit of a far-out suggestion - but could there be complex life in those deep reservoirs. If so could there be a civilization down there? I don't think it is likely. But just mentioning it for completeness.
COULD WE HAVE AN UNDETECTED CIVILIZATION IN OUR OWN OCEAN DEPTHS?
For that matter, I don't think we can say for sure that we are the only intelligent civilization on the Earth.
The giant squids especially are expected to be highly intelligent, perhaps more so than octopuses and squids. Which can lead one to wonder - could they be as intelligent as humans? (In a very different way of course).
If they had a civilization in the ocean depths, we probably wouldn't know yet. Not yet been able to bring any up from the ocean depths alive and keep them in captivity and only a few elusive sightings of them in their natural habitat.
COULD WE HAVE AN UNDETECTED CIVILIZATION ON LAND?
Some human civilizations have been able to survive almost undetected by everyone else until recently. I'm talking here about uncontacted tribes in the rainforest.
If an intelligent species had a very limited range on land, just a few acres left, say, and was also small, shy, fast moving, or well camouflaged, intelligent and scared of humans, we might not know of them yet.
To take an example, many parrots are trapped and killed, or taken for the pet trade. Just suppose (no reason to think that there is) there was some intelligent species of grey parrots. I choose grey parrots here as one suggestion for the next most intelligent species after humans, some possibly may be more intelligent than chimpanzees. Then they'd surely hide away from humans, and spread the word to others in their species that it's best not to be seen by humans.
Could we detect a small remnant civilization of shy reclusive intelligent parrots? Perhaps occupying a small area, just a few acres of the rainforest, say? I think not.
Now - doesn't mean this is likely. But - hard to say that is totally impossible I think.
Even larger creatures - well intelligent creatures seldom get caught, very rare in fossil record, and they'd have friends to get them out of trouble. If they also don't go into building large structures or cutting down trees and clearing land - and are shy and keep out of the way of humans - again - hard to say such creatures absolutely can't exist.
So much of the planet is still not explored in detail. Expeditions are still discovering new small mammals from time to time and they don't know about humans and are not deliberately hiding from us, indeed tend to be over tame in remote areas. Add to the mix that the creatures are hiding deliberately, and are as intelligent as us (say), and it gets much harder to find them. Again, just looking at this as a possibility - not saying it is likely.
(Thanks to Todd Smithgall for touching on this in a comment)
ALPHA CENTAURI - OUR NEAREST STAR
As for Earth like habitable planets around other stars, there is an active search right now for Earth like planets around Alpha Centauri. So that isn't ruled out yet, so our nearest star
These have not been detected, it's just a possibility.
CIVILIZATIONS WITH TECHNOLOGY
As for civilizations with technology - it depends on how quiet their technology is. As it advances, it is likely to get more efficient and quiet. E.g. if they use mainly laser communication, you'd only notice it if it is directed towards you. Also the most efficient way to code up information fills up the frequency spectrum and is close to noise in its structure, so if you do receive their transmissions, it may be broad spectrum and more or less indistinguishable from noise unless you have the key to decipher it.
And then there's also the possibility of some means of communication we don't have yet. Not so long since we first discovered radio waves. Also idea that laser transmission was possible, even more recent. Are there future technologies that we just haven't discovered yet, which when discovered would totally take over from radio and optical communication?
TECHNOLOGICAL ETS IN OUR SOLAR SYSTEM - LEAVE NO FOOTPRINTS
We could have technology like that in our own solar system and be hard put to spot it, either very efficient indistinguishable from noise, or using some method not discovered by us yet.
Though I don't think there is, because the solar system seems totally pristine, no footprints and tracks of alien beings on the Moon for instance and we have already photographed the Apollo tracks from orbit around the Moon - we'd spot anything like that even if they visited it billions of years ago.
Same also for Mars, we frequently photograph our own rover tracks from orbit, and there are no signs at all of any present or ancient tracks by aliens (or Martians). So no sign of anyone on Mars for millions of years at least.
If there were any alien visitors here at any time in the past, through pretty much entire history of our solar system - then they obviously have a policy of minimal impact.
Would have to be a case of: take away your rubbish, no camp fires, and also clean up all traces of your visit when you leave, even your footprints :).
So I would agree, probably not going to find them in our solar system - except - in the icy moon oceans where it could be possible but then would expect them to be non technological. Because it would seem to be likely to be hard to develop tech there - and also because if they did have technology at similar levels to us or beyond, they would have emerged from their oceans and we'd see them easily.
COULD WE DETECT OURSELVES AROUND ANOTHER STAR?
As for whether we could detect ourselves - well very unlikely that a civilization evolves at exactly the same moment in time as us. But since that's part of your question, well someone from the SETI League answers that here: How far can we hear?
A dedicated SETI search could detect us up to 1000 light years away while a small radio telescope such as amateur radio astronomers have would find it a challenge to detect us around the nearest star. The galaxy has a diameter of 100,000 light years, and a thickness of about 1,000 light years - so a dedicated search for us, would be able to cover only around a millionth of the volume of the galaxy.
COULD WE SPOT OURSELVES FURTHER THAN 1000 LIGHT YEARS FROM EARTH
If our clones were actively signalling to us, with focused radio beams, then we'd detect them anywhere in the galaxy, indeed, beyond the galaxy, unless hidden by dust and gas clouds.
But we aren't actively signalling anyone else, except for one very short test transmission some years back, so if you are talking again about clones of us, then you wouldn't spot us that way, and it would take a huge dedicated project to try to signal to most of the habitable planets in the galaxy if they didn't know we were here yet, rather unlikely at our level of technology.
In the search for ETIs, SETI, then with most of the searches, our best chances are of finding ETIs that way would be to find ones that are way ahead of us, and actively transmitting to the entire galaxy or to all habitable planets or some such. Which makes sense as a search strategy, as the chance of finding ETIs that have only just started to develop radio technology, in the last century or so, when they and we have evolved independently for billions of years, is surely tiny.