There are a number of good hotels within walking or (free) trolley distance of the UT campus and the Knoxville Museum of Art. Below are some that we recommend, roughly from least to most expensive.
You should book your hotel as soon as possible: Knoxville is a festival town, as well as a university sports town, and hotels fill up fast year round.
The Volunteer Hotel (right on the campus)
Hampton Inn and Suites Knoxville