San Francisco and Berkeley are excellent for not having a car. In fact, unless you live somewhere where you can park your car for free, it is best not to have a car. http://www.transitinfo.org/ helps you plan your public transit in the Bay Area.
Davis is also good for not having a car since most people ride bikes and the University's transit system is very good. However, you will go bat shit crazy if you don't get outside Davis from time to time. It is a fantastic college town and I LOVED going there, but sometimes you just have to get outside of the town. You can get to the Bay Area on a bus that goes between Berkeley and Davis and that works for a lot of people. You can get into Sacramento on public transit as well, but Sac's transit is not good as the Bay Area.
Washington, DC is a good place for not having a car though it is kind of annoying that the metro doesn't go to Georgetown (you can take buses though). You can catch trains to other east coast cities as well.
Los Angeles is complicated. In some places, the transit is fine, in other places it is horrible (not available/scary). It depends on where you live and where you go to school. There is a very strong car mentality in LA, but public transit can be done. E.g. http://www.bigbluebus.com/busroutes/index.asp the Big Blue Bus, helpful of you got to UCLA.