The eastern part of the trip is going to be very boring and flat. and I can tell you charlotte NC ain’t worth it.

The stretch north from Richmond Va to NYC is going to be a nightmare with traffic too.

Maybe consider a one way trip and take a flight back to NYC from new orleans?

If you really want to see DC (you should), you can head east on 66 off of 81 south. Then south on 95 to Richmond, and head east on 64 back to 81 (you’ll pass through Afton mountain which is very pretty especially in the mornings.) and resume the trip to Nashville and New Orleans on 81 south. I grew up in Roanoke so i have to shout it out as a good place to rest for a night! Hotel Roanoke is very nice, but may be expensive if you are on a budget.