I haven't been to Tennessee or Auburn for baseball, but I am hoping to check both off the list this year. Been to both for football. Knoxville is a nice town -- the only down side I see to this trip is that it is rather early in the year, so the weather might be rather chilly.
I'm passing on UK this time, but we had a good time on the last trip. If you're into bourbon, there are several distilleries to tour, and Lexington has a good amount to offer. This probably isn't one of those places that jumps out to you as a baseball trip, but don't write it off.
The best thing about Arkansas is that you can stay across the street from the ballpark at the Staybridge Suites. That can be a big plus if we have any weather delays.
Everyone should go to MSU at some point to see the ballpark, although their fans seem to think that they invented the game (they are friendly but strangely condescending at times). Starkville is much better suited to hosting baseball crowds than football, as the town can be overwhelmed for football weekends. We usually try to stay within walking distance of the park, which usually means the hotels on, or just off 12 (Comfort Suites or Courtyard by Marriott) or you could rent a place in the Cotton District like derm did for football.