The Deep South has the most distinctive regional culture in the country, and some beautiful old cities. You might look into places like Charleston, Savannah, the Mississippi Delta, and New Orleans.
For national parks and natural sights, some good options are Yellowstone, Yosemite, Bryce Canyon, Grand Teton, the Black Hills, the Adirondacks, and the Everglades.
If you are interested in American history, you might want to visit Boston, Philadelphia, or Civil War sights.