Nashville: Natchez Trace Parkway Bridge or the John Seigenthaler Pedestrian Bridge
The Korean Veterans Memorial Bridge should also be considered, though it’s usually overshadowed by the Seigenthaler.
For Columbia, SC, it’s the Gervais St Bridge carrying US 1 over the Congaree River.
For Greenville, SC, it’s the Liberty Bridge (pedestrian) over the Falls of the Reedy River.
I don’t think Charlotte, NC really has an iconic bridge since it’s the probably the largest city in the country not on a major river. So maybe the I-77 south to I-485 outer fourth-level flyover?
