There are a lot of places in downtown Nashville where it's OK to be there if under 21. However, there's usually is a cutoff time where those younger than 21 have to leave. Some ideas - Roberts Western World (10pm cutoff for under 21) and Wildhorse Saloon.
At Wildhorse, you can only stay past 10pm if you're with an adult. Tootsies is tons of fun, but those under 21 can only stay until 7pm. Don't let that dampen your spirits too much - their live entertainment starts at 10am - that's A.M.!
A couple of other great entertainment venues - 12th & Porter and 3rd & Lindsley - but not sure on what their age requirement is - you'll have to contact them. Oh yea and Rocketown - check out this link to see if this is a venue that might interest you: http://rocketown.com/about