A car in AA is not necessary. I went to grad school there and while i did have a car, many of my friends did not. I was the nice friend who always let them know when i was going to the grovery store!! And really, the main reason I had a car was so I could drive back to my home state of Ohio. Also, I did get a job in my second year that had me driving all over the Detroit area...so the car helped there.
If you go carless, I suggest looking into car share systems, in addition to the public transportation, of course. I am not 100 percent sure that AA has one, but knowing how liberal the city is, I'd place my money on it.
I did live very close to campus (10 minute walk) and never drove to classes. Parking is really hard. But I always heard that if you got a parking ticket, you could pay it that day and it was only $10 or something cheap like that.
Go carless! At least for the first year. You'll be fine.