There's parking at the Music City Center (201 5th Ave S, Nashville, TN 37203), or there's a garage next to the Ryman (401 Commerce St, Nashville, TN 37203). Both are then walkable to the stadium if you use the Pedestrian Bridge. Would then set you up nicely if you wanted to go out after the game on Broadway.
There are construction areas south of the stadium that i have parked at for other events. I"m unsure what their availability is for Titans games. On google maps its labeled as "Premier Parking PSC Metals Cash Lot"