I didn't mention Mexican on there, but I know a couple places that are different...
Let me suggest checking out different neighborhoods (if you have the time, there are interesting shops in these areas too), most have several locally owned restaurants or unique chain ones.
12th South area:
http://www.12south.org/localbusinesses.html
Greenhills area, has the mall, and this place (highend shopping, some really good local eateries, La Paz for Mexican is in this area)
http://www.hillcentergreenhills.com/
The Gulch (near the Frist Center, art and stuff) has some really good restaurants unique to Nashville:
http://www.nashvillegulch.com/
Hillsboro Village area has pedestrian type shopping and places to eat, most if not all locally owned:
http://www.hillsborovillage.com/HVmerchants.htm
Germantown has historic value, and some great small restaurants, just North of the Farmer's Market and Bicentennial Mall
http://www.historicgermantown.org/LINKS_2.html
Good history lesson:
http://www.tennessee.gov/environment/parks/Bicentennial/
East Nashville Neighborhood:
http://www.eastnashville.org/
(Batter'd and Fried is supposed to replicate New England seafood, supposed to have clams servered with the bellies...had to make it reef related right...)
That'll probably keep you busy for awhile...
J. Alexander's (a chain) but has awesome chicken tenders and fries...Otter's Chicken Tenders on Demonbreun are good too...just thinking, kids = tenders at some point.
Dang...I need to go on a diet...LOL