I figured it could be of use to individuals confused on housing (like I am)
There are several neighborhoods in MPLS that are worth looking into. Dinkytown is the area around the U and the closest neighborhood. This might be your best bet. Northeast is presently in the middle of gentrification. This is the new artists district and probably your best bet if you're looking for a good trade off between things to do and cost.
Finally there is Uptown. Uptown is a very love-it-or-hate-it neighborhood I think. There are tons of great bars and opportunities to go out. You're also likely to find something reasonably priced. That said, you do need to cross the river so commuting by bus takes a bit longer. You'll also be surrounded by a mixture of Yuppies and hipsters.
I'd check out those neighborhoods and see what feels best. As a native I have the impression (true or not) that Dinkytown is more inhabited by undergrads and that the majority of grad students live in Uptown or Midway. I'd avoid Midway.
Hope this helps!