Oh boy, you've opened up quite a thread here.
Without a doubt you will want to travel from Florida up to the Smoky Mountains area of western North Carolina. This is home to the famed Tail of the Dragon, however, the area is SO much more than just the Dragon. Check this link and go to the Maps page for a listing of other great roads in the area.
www.tailofthedragon.com
If you decide to go to the Dragon, I highly recommend that your group stay at least one night at the Historic Tapoco Lodge.
www.tapocolodge.com The rates include a high end multi course dinner and cook to order breakfast at a site that is 3 miles from the Dragon.
Nearby is the start of the Blue Ridge Parkway outside Cherokee, NC. It is a 468 mile limited access scenic road that runs along the spine of the Appalachian Mountains into central Virginia. Little Switzerland, NC is a fabulous stop along the Parkway. At the northern end of the Parkway you drop off in the middle of Virginia Wine Country. Many of the wineries in the region offer B&B accommodations.
By now you are about 100 miles outside of Washington, DC. If a visit to our nation's capital and all of the historical sites and museums interest you, this is your opportunity.
For north of DC I will turn if over to other Captains for their recommendations.