Kinda funny that we like vacationing where YOU live! hahahaa We've been to the OB several times in NC and everywhere down to Tybee Island, GA and in between. Lots to do over there.
You're in SC. Have you been to the Smokies? We've been there probably 10 times. Lots of good day hikes in that park.
Mammoth Cave. There's several different tours of varying times and difficulties. It's cool in summer and warm in winter down there.
If you go out to Rapid City, SD, there's probably 5-6 days worth of stuff to do there.
Mount Rushmore
Crazy Horse(not a National Park, but 10 times more impressive than Rushmore, in my opinion)
Devil's Tower
Some caves.
Badlands
Yellowstone was our favorite. But be prepared for lots of traffic in season and gosh help you if you get caught in a bear jam (bear stops traffic).
Little Bighorn battlefield.
You ever been up to DC? I highly recommend it, if not. Stay in a town on the outskirts and ride the subway in daily to the national mall. The subways are clean, safe, and easy to use. I had my kids plan the subway route and take me to the mall to see if they could get around if they got lost. No problem for them at all.
Gettysburg, PA is a must. Great park! You can drive, stop and walk all day long. 2 days if you read a lot.
Grand Canyon was OK. We had more fun flying into Phoenix, driving south to Tucson to the San Javier mission, then north to the Grand Canyon, but stopping at all of the cliff dwellings on the right on the way up, and the right on the way back to Phoenix. There's a LOT to see in AZ.
Big trees in CA.
Our to do trip would be to fly out to LA, then drive north to Canada along the ocean, then fly home. Would take a couple weeks for us, though.