Well, on a 800 mile circle around Arkansas are several of my favorites...they are all park related, of course! Just a couple today.
The "Gold Coast" of southeast Georgia. Savannah is a neat city to visit just north of there, but the main attraction is the low country south of the city. I recommend checking out the historic Jekyll Island Club on the island of the same name (reasonable rates to stay there even!) Another neat area is Cumberland Island National Seashore, a NPS area you take a ferry to from the town of St. Mary.
There are airports on St. Simons, Jekyll Island, and in St. Marys. There is a grass strip on Cumberland Island but Google Earth shows X's on it - no doubt the Park Service has closed it once they gained title from the former private owners as they are w'ont to do. Fly into St Marys, take the ferry over and camp a night or two. St. Simons is the most "touristy." Cumberland is the most beautiful! Jekyll and St Simons have golf if you are into that.
http://www.rvfreewheelin.com/cumberland_island.htm
http://www.manchesteronline.co.uk/travel/reviews/s/127/127572_us_georgias_gold_coast.html
Do you have Google Earth installed? The placemarks are attached below.
Next - a closer one is Rough River State Park in Kentucky. Very aviation friendly.
http://parks.ky.gov/resortparks/rr/
The Fontana/Nantahala area of NC is very beautiful. Fly over the Great Smoky Mountains National Park to Nantahala, North Carolina, land at "Ferguson Municipal" and stay at the Nantahala Outdoor Center and get in some great whitewater rafting. Neat place to stay.
www.noc.com
The other direction...where does one start?!?
I would recommend easing your way into mountain flying in Colorado or NM - there are some flight tourism companies out there that can help.
Finally, here's a neat website -
www.adventurepilot.com
You can do your own search!
Oops, the forum software doesn't allow for the attachment of Google Earth placemarks...I'll have to look into that.