Try Bobby Q's...... they're at 1070 N. Washington in Cookeville. They specialize in BBQ and catfish. It's a favorite spot for locals. The waitresses are very friendly and helpful. We've eaten there several times- stop whenever we're on our way through. I haven't had anything but their pork bbq..... I figure if that's their name, that's what I'm having. It was very good- they have a couple of different sauces, I think one hot and one sweet. Sides are great, too.
Bobby Q's is outstanding. Try the ribs, chicken, or pulled pork. They have a hot slaw called poolroom slaw that is very good (or you can get it mixed half and half with regular slaw for a cooler version). Their banana pudding has been featured in Ladies Home Journal.
El Tapatio has fine Mexican food - there are two locations in Cookeville; one on Jefferson Avenue and one on Willow Avenue.
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.