There is a really large, very new apartment building just across the street from the law building called Knoxville Place. It is sort of an animal house sometimes, but it has its own parking garage, and you can't get any more convenient than across the street.
There is also a place called the Raillery with really big one bedrooms just west of campus, off of Papermill road. It is probably less than a 10 minute drive. Check out http://www.knoxapts.com
Just a tip - don't live south of the river unless you are really cheap. There is cheap student housing there, but it isn't very convenient to anything, and the hillbilly population in that part of town is rather large.