The Moon for sure. Yes they went to the Moon "because it is hard" - is a good bit of rhetoric in a speech. But doesn't mean that you just out and do the most impossible thing you can find to do.
In case of Apollo they did many previous missions to Earth orbit, around the Moon etc before they went to the Lunar surface.
So - even if you are planning to go to Mars eventually you need easier objectives first. And the Moon is the obvious stepping stone on our way to anywhere in space.
Either the Moon - or - in orbit around the Moon - or in the L1 or L2 positions in gravitational equilibrium above near and far sides of the Moon (sort of a bit like geostationary orbit for the Moon).
MOON ITSELF STILL A MAJOR CHALLENGE JUST TO GET THERE
Indeed - the Moon is also quite a challenge. We can't just get out the 1960s hardware and fly that. Would need to make new rockets, and we'd need at least several previous test launches, just as for Apollo, before it's reasonably safe to send a human to the surface of the Moon once again.
Our hardware is more capable - but also more complex - in some ways - that means there is more to go wrong. After all the rather venerable Soyuz is still the favoured way to get humans into space - because of its long history and safety record.
It might take a while to get modern rockets with similar assurance of reliability for humans as the old Apollo hardware.
SECOND CHALLENGE - TO STAY THERE FOR YEARS ON END ONCE WE GET THERE
Once we can have manned outposts on the Moon or in orbit around the Moon, or in L1 or L2 above the lunar surface, that last for years on end with no resupply from Earth - we can think about going to other places in the solar system.
But to launch out to Mars even the shortest flyby as in Inspiration Mars - I was keen on the idea when I first heard it - but on reflecting, it really seems like madness to do that first.
We have never sent anyone further than LEO since Apollo - and never sent anyone anywhere at all without resource to continual resupply from Earth every few months and return of wastes to Earth atmosphere. And not just small amounts, many tons of resupply and waste disposal per astronaut.
SOYUZ LIFEBOAT
And as well as that, they have a Soyuz spacecraft constantly docked to the ISS which they can use to fly back to Earth at a moments notice if a disaster were to strike.
The idea that suddenly we can send expeditions to Mars orbit, with
- on reflection - it seems like madness :).
CHALLENGES
Major human factor challenges include
So - we have to crack this closer to Earth first. Anything else is a recipe for disaster and tragedy in my view.
SOME QUESTIONS FOR MARS FIRST ENTHUSIASTS
Do you think that we could send a mission to the Moon - or to L1 or L2 - and just leave it there for two or three years without resupply from Earth with present day technology?
If so - if we have the technology for interplanetary flight already - or nearly ready - why do we spend so much every year on continually changing the crew of the ISS and resupplying them from Earth?
Why do we think a lifeboat is so important for the ISS, that they can get back to Earth within hours?
If you hesitate at the prospect of a human crew spending two or three years at the L2 position on far side of the Moon with no resupply from Earth - why do you think that they will fare better on a mission to Mars?
INTERESTING MOON
Luckily the Moon has turned out to be far more interesting than we realised before. And - it has hardly been explored at all. Only one geologist has ever been there, on Apollo 17 and he spent a few short hours on the surface. There's a huge amount to be done on the Moon.
ROBOTIC MARS
Meanwhile we do have a number of exciting missions to Mars. Can't do as much as robots controlled telerobotically by humans.
But will get increasingly more capable and autonomous also.
For more on this see my Case For Moon - New Positive Future For Humans In Space - Open Ended With Planetary Protection At Its Heart