I suggest staying in downtown Knoxville so you can easily walk to museums, restaurants, shopping and theaters. My recommendations include:
The Oliver Hotel: This is the place to stay in Knoxville. It is an historic old hotel in the heart of downtown. 407 Union Ave. Tupelo Honey Cafe is in the lower level plus they have a great cocktail lounge, the Peter Kern Library, right off the lobby. From here it is an easy walk to other restaurants and shops downtown.
The Tennessean is a new boutique hotel opened in April 2017 with contemporary rooms and a lovely Drawing Room on the second floor featuring cocktails and breakfast in the mornings. I will definitely stay there on my next trip. 531 Henley St.
Larger hotels that are good if you want to be downtown include the Hilton Knoxville at 501 W. Church Ave. The rooms are comfortable and contemporary and they have a Starbucks Coffee store in the lobby with both indoor and outdoor seating. There is also Marble City Kitchen and the Firefly bar. I enjoyed the breakfast buffet at Marble City Kitchen on my last morning before driving to Lexington, KY. They do offer valet overnight parking. I loved being able to park my car and walk everywhere downtown without having to drive until the morning I left.
The Crowne Plaza Knoxville is also in a great location from which to walk and explore downtown and Market Square. 401 W. Summit Hill Dr.
Southwest of downtown near the University of Tennessee, at 1706 Cumberland Ave., is the recently opened Graduate Knoxville. I really like this Chicago based hotel chain that has targeted major university towns around the country. They have the Poindexter cafe off the lobby for coffee drinks, breakfast sandwiches, salads and more plus the western-inspired Saloon 16 bar.