Yes! Ann Arbor has a great mass transit system, and is a very compact city. Having a car is, as always, really nice, but you can live happily in A2 without one - and parking downtown is a bear, so you may actually be better off. read more
If you live downtown Ann Arbor, you don't need a car. But groceries are lacking. But there are quite a few zipcars to hit Krogers or Meijers. You could take the AATA to Krogers or the Ann Arbor Saline Meijers. Theres also a nice co-op by Kerrytown. read more