Bobby Q's is a good choice for BBQ. Also Moogie's which is really only a drive through place, but has pretty tasty stuff...and you could always take your food to a park or something if it's nice.

Some other options:
Maddux Station, bills itself as contemporary American bistro type fare. Nice casual atmosphere, good food from my experiences. They have a website madduxstation.com with a menu.

India Palace, good for the lunch buffet and dinner as well.

Spankie's, a cookeville institution with a pretty eclectic menu.

Crawdaddie's also a pretty eclectic menu with a few Louisiana/Cajun inspired dishes.

Mauricio's or Mama Rosa's for Italian.

House of Thai, usually pretty consistent.

Taiko (sushi)...owned by the same family as House of Thai and pretty good considering it's a landlocked state.

Village Kitchen, 13th St. Kountry Cafe, Maddie's Place, or Cracker Barrel(chain) for typically southern food.

Dipsy Doodle, typical American, which is a little outside of cookeville, but well worth the short drive.

Hope this helps...I would think you can google the addresses of almost all of these.