Get a map of Madison. Hang the map on a wall. Throw a dart. Look for housing wherever the dart lands.
More or less, that was my strategy for finding housing when coming to University of Wisconsin-Madison. I did, however, consider the proximity to classes, Wisconsin Capitol, and undergraduates in addition to where my dart landed. The apartment I rented was in the Bassett Neighborhood and turned out to be decent enough.
The Bassett Neighborhood is just southwest of the Capitol and only a long 25 minute walk to class (10 minute bike ride). Other than a spring semester block party (Mifflin) and random undergrad parties (a few a semester), the neighborhood is quiet enough.
The neighborhood has quite a history, such as housing the La Follette family for many years (Capitol Neighborhoods, Inc). Many of the old buildings still exist, but are converted to student housing and show much wear and tear. Most importantly, in my opinion, is the neighborhood’s few – but great – businesses. Capitol Centre Foods, the only downtown, full grocery store, is within walking distance. Several neighborly coffee shops and bars are also scattered throughout. (I must admit, the Echo Tap Bar and Grill is one of my favorite bars; despite great deals, it is a place where you see friendly locals instead of drunken college debauchery.)
All in all, I recommend the Bassett Neighborhood. Rent is not cheap, but not ridiculous. Location is decent – not the best, but not the worst. There are other nice places to live in Madison, true, but they miss out on being a few blocks away from the Echo Tap.