Ok, There's the UT married students apts. on sutherland ave. then there's some UT apts. off Sevier ave. in S. Knoxville. If not those then you have some apts. on Ft.sanders hill,Close to campus but very little parking. If you want an apt away from campus then you can try deep South Knox. The area just accross the river is a rough area. Or N.E. out past West Haven. (Western Ave.) The apts. out West are pricey, but there are some that are not. just be careful account most are inhabited by the illegals. Stay out of E.Knoxville altogether.
This is about the best I can do for you. I haven't actually lived in K-Town for a while but most of my family is there. Good Luck in your search.

Bill