Bearded Iris, Southern Grist, Yazoo, Jackalope, Smith and Lentz, supposedly Little Harpeth is has very good lagers now since they got a new brewer (it once was diacetyl city) so it might be worth checking out.
Make sure you get some Hot chicken! Prince's is probably the best. But I also really like Party Fowl even though it is a small chain. The chicken is great. Hattie B's is pretty popular but I didn't love it but maybe it was just an off day.
The Parthenon is worth the visit as is the Frist Art museum.