If you'll be near the Arena, it's just a hop over to Broadway. Lots of bars on Broadway and down Second Ave. Most of those places will carry the usual Nashville locals; Yazoo, Black Abbey, Jackalope, Little Harpeth. Rock Bottom is a restaurant that brews their own (way too big to call it a brew pub) that is worth checking out. They are right near the river with a big rooftop patio. The Hard Rock Cafe is right across the street from there. BB King has a restaurant on 2nd for some good ribs and music. Everything I've mentioned is walking distance from Bridgestone so its easy to get out and explore.
If you get away from Downtown, a short trip to Corsair distillery in Marathon Village is worth the trip. I haven't been up there in a while, but the restaurant pickins were slim last time I went.