Personally don't think have to rush into it given the increasing capabilities of our robots which are of course, much more comfortable and safe in space conditions than we are.
But if we do, then:
1. Moon, especially peaks of eternal light at the poles. This depends a bit on whether humans can live long term reasonable health in lunar gravity. If not, then may need to have revolving habitats, or habitats in continuous trains running around on tracks on the surface etc for artificial gravity, if so Moon maybe not so likely for more than short term stays because easier to do things like that in free space.
2. L 1 and L2 positions close to the Moon. Far easier to get to / from from Earth, safer. I think that might be first actually rather than Moon.
These would be small to start with but eventally, use all the ideas of building habitats in free space, Stanford Toruses etc if they got really big. Advantage is so close to the Moon - easy to operate telerobotics on the surface.
But then might be that technology develops to the point where the robots are semi autonomous and easy to control from Earth and you don't really need humans there.
3. Asteroid miners, maybe, - but many of the NEOs that we'd want to mine spend years a long way away from the Earth. So would people want to live out there, or would it perhaps be mainly automated, returning materials to LEO for processing?
4. If we discover life on Mars, or other interesting stuff there that needs closeup scrutiny - then expect a colony of scientists living in orbit around Mars closeup to be able to study it properly - not on the surface because of planetary protection.
4. If we can crack closed system habitats (able to grow all their own food also etc) and cosmic radiation shielding and artificial gravity - and - I just don't know how hard that is as nobody has tried. Might be that a 10 year project would solve everything, or might take several decades. But if we can - you'd get self contained Antartica type settlements, research stations, that you could send on long voyages.
Even to Pluto if humans can be found able to withstand the decade or so of travel time to get there. Jupiter, Saturn, Neptune and Triton, could have small outposts anywhere.
But on other hand, maybe it will all be telerobotics and artificial real time. And may only have an occasional spaceflight by humans apart from tourists.
Don't know, many things would depend on other things.
Just ideas. With future prediction of course nearly always you get it wrong :). Reality not at all what you imagined. The 2010s are nothing like I expected in the 1970s :).