Ann Arbor has two separate public transportation systems, TheRide and TheLink, the latter of which is out of service for now. Rumor has it the city pulled its funding. TheRide is still operating, however, and you can ride it downtown and back. I'm not sure how convenient it would be for you to use to get to the law school every morning. Since it does get cold in the winter (5 to 25 F), it's not the best weather for long walks or standing at a bus stop. If you can afford it, I'd recommend a car.
If you want to walk--it's good exercise, after all--there is an apartment complex within walking distance of the law school--Greenbrier Apartments--and another one about a mile away--Windemere Park Apartments. Windemere Park Apartments, in my humble opinion, is a much nicer place to live (I've lived here for two years) and the new owners are benevolent towards Ave Maria Students. Windemere is also nicer looking than Greenbrier. You can call the office at (734) 662-0330 and ask about rates. Tell them you'll be going to Ave Maria in the fall. I think they allow pets for a fee.
If you get a car, 4WD is superior to 2WD; it gives you more control and you, as a result, can be a more confident, aggressive driver. But most cars in Ann Arbor (more than half from what I see upon casual observation) are not 4WD (or AWD), and people seem to do just fine. I've driven a 2WD car here for two winters and been in only three accidents. j/k. If you opt for a 2WD vehicle, just make sure it's front-wheel drive.
For getting a top-quality legal education in a uniquely moral environment Ave Maria is an excellent school.