Moved to Chattanooga 2 years ago from Houston. We love it here. If you are looking for great BBQ you will be dissappointed, especially if you've been to great BBQ places in Memphis or Texas, but there are some great places to eat. Public House, Tony's Pastaria, or The Boathouse are reasonably priced with great food. If you only have 1 meal, I suggest Public House. If you want a good breakfast place, try Maple Street Biscuit Co., you won't regret it.

As for things to do, the Aqarium is great. The saltwater building is not ok, but nothing special, so if you are short on time, skip it. The freshwater aquarium is much better and unique. Gives a great overview of the Tennessee River watershed which is the most biodiverse freshwater system in North America.

While you are downtown and have some time, the walking bridge connects you to the north shore. Cooley park has an old wooden carousel with animals carved locally at a carousel animal carving school. Each one is beautiful one of a kind.

Rock City is...different, but fun. Especially if you have smaller children. 

Skip a Ruby Falls.

Chickamauga battlefield is beautiful and was the first military park established. Bike it, if you can. chattanooga also has a national cemetery that is beautiful. Several revolutionary war and 1812 vets are buried there, along with the famous WWII medic Desmond Doss.

There are plenty of hikes in the area.

http://openchattanooga.com/chamap/map

Hope you like it! It's small but has character.