Chattanooga's oldest attraction is the Incline Railway, which brings visitors up to the top of Lookout Mountain. The vintage trolley cars are on a steep 72% grade, but seats face outward so you can see yourself rise above the trees to see the city from above.
In the 1800s, there was a luxury resort on top of the mountain, which you accessed by the railway. Now the top end is home to a Civil War battlefield, while the bottom is in the St. Elmo neighborhood, which has lots of bars, restaurants and shops.
You can purchase combination tickets with other nearby attractions like Ruby Falls and Rock City.