Dave: Take I-95 to I-40 to Wilmington, NC and pick up US 17 south along the coast.
Rt 1, after Washington DC, goes way inland through Aiken, SC and Augusta, Ga over towards Atlanta and comes back out on the coast near Jacksonville, going through every podunk town along the way and the roads, while flat, are straight for hour after hour. I've traveled a lot of it and it's not all that scenic.
US-17, OTOH, starts in Fredricksburg and travels along the coast through Norfolk, VA (the only busy area until you reach Charleston, SC) and lots of salt marsh areas, through New Bern (you could visit Nicholas Sparks, who lives there), Myrtle Beach, Charleston, bypassing Beaufort, SC (but worth the detour to pick up SC-170 past Hilton Head and into Savannah), then on down through Savannah but switch over to GA-25 out of south Savannah all the way to Brunswick, Georgia. RT-25 is one of THE most scenic marshland routes along the entire East Coast and everyone who travels inland on I-95 misses it. From Brunswick you can either stay on 25 to connect with 17 all the way to Jacksonville (but I have not traveled that stretch) OR hop over to I-95 and blast down to J'ville that way - either way, you pick up A1A and then RT-1 south of J'Ville.
Most of RT-17 and all of RT-25 travel through marsh-side or coast-side villages except for the stretch through Mt. Pleasant (stop and see Lane and go for BBQ or seafood) and Charleston, SC. Make sure you stop in Darien, GA, on the coast - it's a fishing village like those in Nova Scotia, but on the Georgia coast - VERY picturesque and worth the trip right there, just for the three local restaurants.
How's that sound?