Hi! We visited Chattanooga this past summer on our way up to OH to visit family. (Good halfway point when driving from FL!).
Since we're a family of 5, one bathroom is usually a pain, so we stayed at the Residence Inn that is within walking distance (really close!) to the Aquarium and Children's Museum. We had a 2 bedroom suite with a full kitchen. Our boys (9 and 12 at the time) shared one bedroom w/a full bath, my DH and I shared the other bedroom w/another full bath, and our DD6 slept on the queen sized sofa bed. The kitchen had a full size fridge, dishwasher, stove, and microwave.
They had an indoor pool and a great breakfast (cold and hot offerings) every morning. There was also an evening snack before dinner time.
The hotel was very clean, reasonable for the amount of space and amenities we had, and close to everything in downtown we wanted to do. You can ride the trolley (right across the street) to the Choo Choo hotel to see the train. The movie theaters are also within walking distance and we ate at Mellow Mushroom one night (great pizza, we have one here where we live) and got discount tickets for the movies. Good deal.
I would definitely recommend the Residence Inn, especially if you have a little one who sleeps better in a "quiet" room, a family that doesn't do well on one bathroom, parents who want some privacy (wink wink), and a full kitchen to keep snacks and other items cold and available to save some $. There really aren't any hotels for families up on Lookout Mountain, although if you and DH ever get a chance to getaway by yourselves, the Chanticleer Inn is very romantic and perfect for a trip w/o the kiddos!
Chattanooga is awesome - My DH and I visited there "pre-kid" (stayed at the Chanticleer Inn) and wanted to share all it has to offer with our kids, even "hokey" Ruby Falls and Rock City. You'll have a great time there!