Romantic view No. 1: the top of Lookout Mountain. You can see three states and get a fantastic look at the Tennessee River as it winds through the Chattanooga downtown. Romantic view No. 2: The Hunter Museum of American Art. From the windows just inside, look out at the water and Chattanooga's picturesque bridges. Art is everywhere in Chattanooga — from the sculpture gardens to the aquarium to the ice cream just down the street.