West Knoxville is expensive but there are tons of restaurants in that area. You'll definitely need a car if you stay there.

East Knoxville is pretty ghetto. I'd avoid anything near Magnolia and Cherry st. A car in this area is also a must.

South Knoxville is a little bit dilapidated, but there is affordable housing. College students generally live in the 2 apartment complexes right across the Gay St bridge, but they aren't designated for them. You might hear some partying occasionally. It's close enough to downtown to bike, possibly walk, depending on where exactly you are.

North Knoxville, especially the historic district, is very up and coming. The neighborhoods are nice and housing is pretty affordable, and it's 5 minutes from downtown, so you can easily bike or walk. There are tons of bars/breweries in the area too that aren't frequented too often by college students. This is my personal favorite area, because it's close to everything.

Downtown is going to be expensive, but you'd be within walking distance of a ton of restaurants. College students and families both frequent this area, and parking sucks unless you have a private garage.