I've heard good things about the "Tail of the Dragon". It's a section of US 129 between Tennessee and North Carolina. It has 318 curves is 11 miles. It also has a 30 MPH speed limit, and I hear it's strictly enforced. I recently saw an article on "11 coolest small cities" in the US. Sedona, Arizona and Asheville, North Carolina were on the list, and would be easy stops to add to your route if you chose to drive the Dragon. You could also easily add in stops in Washington, DC and Gettysburg, PA.
I'm sure others here will also chime in with some suggestions.
Edit: It adds distance and tolls, but Chincoteague, VA is a small town I love to visit, including a visit to Assateague Island to see the ponies and other wildlife as well as the beach. Adding the stop here will allow you to see the Chesapeake Bay and Atlantic Ocean. It will take you across the
Chesapeake Bay Bridge Tunnel and there are several options for continuing north, the "Bay Bridge" would be the best option, if you're including a stop in Washington, DC.