This is the answer.
Saloon 16 is absolutely awesome and worth visiting at least once just to see the incredible memorabilia on the walls, but at its core you're going to a casual hotel bar with mediocre food (cheese bings aside, you might as well eat at Half Barrel or Cool Beans) and standard drinks while paying a hefty Tennessee tax to do so. The television situation in there leaves a lot to be desired as well, so it wouldn't be my choice to actually watch a game.
Lonesome Dove is still the best restaurant downtown in my book (Emilia and Oliver Royale are also great if you'd prefer being in Market Square, don't buy into the J.C. Holdway hype) so you'd be hard pressed to go wrong there as GBOVols said, and the relatively-new flat screens at Barley's have served me well for watching mid-day tennis and such when in town. Barley's will likely put the game on a projector, too, and my assumption is that the band they have scheduled for 10:00 p.m. will be held until the end of the game but I'd probably call to check about that because the last thing I'd want is a close battle in the 4th quarter upended by some "jazz and psychedelia" music.
If Barley's doesn't work for whatever reason, Old City Sports Bar skews very young so I would recommend trying to get a seat at Tommy Trent's on the corner of Market Square or begrudgingly paying a visit to Skybox on the 400 block of Gay St.