Where is the best place to park when U.T. has a home game?

The State Street, Market Square, and Dwight Kessler garages are all free during home games. Also, street parking on Gay and many of the surrounding spaces are pay, but a 2 hour limit, so they turn over easily and aren't occupied by folks attending the game. See https://www.downtownknoxville.org/explore/parking/?t[]=37

There's paid parking everywhere. It gets cheaper the further you're willing to walk, and if you don't mind being blocked in.