We've used 2 in the area: Raccoon Mtn Campground. Our thoughts: Thought it has a cave, go-carts, and some nice views, it is filled with permanent campers so expect fridges, porches, and general junk around the campground. Not a bad place, but cramped and feels more like a trailer park.
Holiday Inn Travel Park -- while Raccoon Mtn is on the north side of Chattanooga, Holiday is on the south side, literally just over the border into Georgia. Don't worry...you are still in Chattanooga. We love this place...long wide pull thrus, and next to a civil war cemetery. Costs more, but we liked it more. We stay at this one about once per year on way to Florida.
Things to do in area: Rock City, Lookout Mountain. Spend a day here...it's worth it! Ruby Falls, a cave, and more in that one area. Chattanooga Choo Choo hotel downtown. Worth a visit! Train yard in back with historical trains. Lobby is nice, and a nice restaurant inside. There is more, but these to us are the highlights.
Have fun!