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.
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.
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.