Richmond, VA is somewhat south, so I would head south first. Check out Colorado, New Mexico, and even Arizona. Plenty of sights to see there -- the Rockies, desert, etc. Interesting cities/towns such as Sedona, Santa Fe, etc. True you will be a bit too far south, but worth it. Then head east. You can end up on the Blue Ridge Parkway, taking you near Charlottesville, VA. A different path is coming up the eastern coast, visiting Savannah, GA and Charleston, SC.

New Orleans is obviously worth visiting, though it will take you further south yet out of your way.

Salt Lake City: If you glimpse at the lake itself, it is worth 5-10 minutes. I found Temple Square (home of the Mormons) to be worth a visit for a couple of hours but other than that I could find nothing to do in SLC, like nothing.