I grew up in Greenville SC so have spent a lot of time in both states. If you can only visit one place in each state I would go to Asheville and tour the Biltmore Estate and take a hike on the Blue Ridge Parkway, and then Charleston SC and tour the old part of the city and visit a beach. You'd get a little of the Carolina mountains and a little of the Carolina low country. Nag's Head, Outer Banks, Hilton Head, etc. are all nice also, but I think Charleston is more unique to SC and Biltmore is more unique to NC. There are cool mountains and beaches lots of places, but you won't find anything much like these anywhere else.
