Well, there's a housing area called the 'Flop' where a lot of new arrivals stay until they figure out other accomodations. It's communal and a little tight-packed, so, um, it might not be exactly what you're looking for.

[HULK SMASH in the middle of a crowded dorm is not likely to endear the locals to the ship arrivals any, after all.]

Other than that, there are a lot of empty apartments that can be reclaimed -- Jane and I, and ostensibly Tony, are sharing one. I'm not sure where Captain Rogers is staying. They're private and can be as close or as far from the centres of activity as you like, but it does mean having to do some scrounging for furnishings, and potentially trading for things like a generator if you want power.