I just moved from Memphis after spending 5 years there for undergrad at the University of Memphis, and I moved to a new place every year and so got a decent feel for the city.
There are a few areas where UoM students typically live: Campus, Cordova, Midtown
Campus: the UoM is mainly a "commuter school" so very little of the student population actually lives on campus (id guess <10%). And its expensive compared to living in the city. There are a lot of resedential neighborhoods nearby campus that make for good student housing because its so cheap but be careful which street its on, some are OK, some are scary.
Cordova: after living on campus for a year, I moved to Cordova which is probably the best value/cost ratio. Its clean, safe (for Memphis), lots of shopping nearby, and plenty of reasonably priced apartment complexes. The disadvantage is mainly the distance. Its about a 20min drive down the highway to campus which becomes ~45min in 8am traffick. Also, its is described by some as "chainy", "generic", or just boring. Lots of chain restaurants and hardly any nightlife to speak of.
Midtown: the last couple years I spent moving around midtown. The trick in Midtown is finding a cool place to live where you wont get shot. Like other posters have said its very splotchy, one street is nice and homey, the next is gang territory. But beyond that, Midtown is great because its has a good nightlife, lots of cafes and interesting restaurants, etc. The population there tends to be younger, more open minded, progressive, "culturaly aware" (whatever that means) than the rest of Memphis.
as for other places: Downtown (too far away), Germantown (too expensive), Bartlett (boring).
Conclusion, if your main concern is: convenience (neighborhood nearby campus), cost or saftey (Cordova/Bartlett), good times (Midtown, esp near cooper-young intersection)
Of course, this is all IMHO. I have much more to say about Memphis, but will save that for another post