I think that U of Chicago is a great school to go to if you don't have a car. They have a very nice shuttle system and most students live within five blocks of the school, so if you don't want to walk home late at night, you can always take the shuttle. The neighborhood isn't so metropolitan, but it is feasible to go downtown if you want to go out.
Hopkins isn't too bad either--we have a shuttle system that picks up from 3 or 4 different neighborhoods, so as long as you can walk to the shuttle stop, it's not too bad. I'm going to be dorming this year, so I'll be living right across the street from the hospital/campus. But even with apartments, it's not too hard to find one in one of the 4 areas. Oh yeah, and we're located in Baltimore--the "greatest city in America"...that's what our public benches say.
You *could* do WashU without a car but St Louis has essentially no public transport and the university shuttle system is very limited. You would also be very, very bored - St Louis is not the most exciting place in the first place, but what is here is very spread out so without a car I can't imagine living here.