You're going to get VERY different answers depending on personal characteristics/preferences.
Ex: I hate apartment complexes. Hate them. I'm not fond of the 'burbs, so I prefer to be w/in city limits. I have two large dogs, so that a) limits the places I can rent and b) influences the type of setting I look for. Neighborhood and "character" and setting and price (and in-home laundry) are really important to me, so I sacrifice on things like proximity. LOTS of other people have different needs and rank these things differently. You'll hear plenty of people tell you that you must must must be w/in a 5 minute walk of the law school, but that's a non-starter as far as I'm concerned.
Anyway, my super roundabout point is that you're better off figuring out what types of things are important to you, do a little research on Ann Arbor's neighborhoods, and then ask for advice. Otherwise anything I tell you now will be wildly subjective based on my likes/dislikes/whathaveyou.
Now that I've refused to be useful, I'll share some very helpful links. These both tell you about A2's neighborhoods and are a great starting place. I find the umich site slightly better but it's probably worth checking both. http://www.offcampus.housing.umich.edu/lt/map.cfmhttp://www.arborweb.com/cg/t1300.html
Oh, and for point of reference, I live in (and love!) neighborhood 3 on the school's map.