My overall suggestion would be to start somewhere further north and end somewhere further north, from both a scenery and climate standpoint. Or do a north-south, or south-north route. (My own longest tours in North America have been north-south & south-north.) But since I still don't know what your motivations are and whether it's absolutely essential to you that you ride eastward to reach the Atlantic Ocean, it's less likely that I can give you suggestions which might be helpful for you.

I've been across Tennessee but only was in northern Mississippi and northern Alabama, not the central parts. But from what I saw, Tennessee was more scenic than northern MS/AL. But scenic may not be relevant to you, though you haven't said anything one way or another about that. If the end-point has to be in the SE, I'd aim for Savannah, which is perhaps the prettiest town in the South (along with Charleston, SC).

As for southern Colorado vs. northern NM, there are nice areas in both. Overall, I found southern CO more scenic, and northern NM more interesting from a cultural standpoint. But once again, both of those attributes may not be relevant to you, but I can't be sure unless you tell us.