For the person who mentioned Binghamton University - biking is legal on the Vestal Parkway, but no one does it (for the most part) because too many people have been killed walking/biking there. But, there is a much smaller, safer road that runs parallel to the parkway (Old Vestal Rd.), so you could ride a bike to all the places you need to go without fear of death. I've always had access to a car in Binghamton, but I have friends who live there without cars. Challenging, but definitely doable.
Ithaca, NY: Really, really easy to live in town without a car. Public transportation really is very good, especially if you are living on the college campuses. If you're out late at night, you may have to take a cab, but the town is very compact and most of restaurants/bars/etc are within walking distance of Cornell. Ithaca College is a lot more isolated. I have lots of friends there that bike everywhere. Yes, the town is almost entirely made of hills, but honestly, there are something like 25,000 students + local residents walking up and down those hills, so you can do it, too. Getting out of town without a car is a bit more difficult, but greyhound makes it easy to get to NYC at least.
Washington, D.C.: As everyone's said, fabulous without a car. Just a word about Georgetown. Yeah, it's not on the metro, blah blah, but really - bus service into the area is excellent, especially the Circulator. The Rosslyn metro stop is 1 mile away (15 minutes) over a very scenic bridge. There are multiple shuttles that take you to the Dupont, GWU, and Rosslyn metro stops if you can't walk for some reason. So really, it's not as cut off as people make it out to be. Also, I have a lot of friends who bike in DC without any real problems. I'm actually moving out of the District this month because my new job requires me to have a van, and I have no where to park it.