Moku: Those are really good suggestions. I live not too far away from MEM, but can't afford to rent planes as a hobby.
MikeKilo: As for further destinations, you might also try northeast or north central Arkansas. Don't know if you want to take time to rent a canoe on the beautiful White or Buffalo Rivers. Jonesboro is in eastern AR. Northwest of it is the small town of Hardy, with the smaller Spring River. Jonesboro (JBR: 6200', ILS/VOR/GPS).
Mountain Home (BPK) is in an attractive area of rolling hills. My "Pilots Express Airport-FBO Directory" say it has 5001', VOR/GPS/RNAV.
Northwest AR might be too far for your style, but Fayetteville is in an attractive area, and has the old airport FYV (terrain by the airport) and the newer XNA. Hot Springs (HOT) is real nice, 46 nm southwest of Little Rock (LIT VOR). LIT airport is about 120 miles on the MEM 259* radial. There is a small mountain not far west of Little Rock, but this stands all by itself: Mt. Petit Jean-good place to hike or rent a cabin. Notice that the Ozarks are to the north. A Trans-Texas Int'l Convair 640 (RR Dart engines) chose to make a VFR departure years ago from LIT, and while deviating around weather, because the crew assumed that there were no hills south of the Ozarks, hit Petit Jean about 200' below the top.
Going e/northeast to Nashville (BNA/JWN/M88: about 180 miles, 070 radial from MEM VOR) will put you at the beginning of the rolling hills of Tennessee. There is a nice area somewhere south of Nashville, probably in Hendersonville, or Murfreesboro, one of which has nice rolling terrain. Have seen the hills straight ahead a good distance, when departing BNA on runways 20L/C/R.
Birmingham, AL (BHM is also in an attractive patch of rolling terrain, with low hills in most quadrants from the main airport). 117* radial from MEM VOR. Huntsville (HSV) has the interesting NASA Space center and an excellent, round, IMAX movie theater.
The coast of southern Alabama had some hurricane damage, but not as much as Pensacola, as far as the panhandle is concerned. My parents live east of Mobile Bay. NAS Pensacola has some auxilary tng fields for T-34s etc so plan well ahead, with MOAs for aerobatics west to Mobile Bay. You might make some phone calls before planning to park a plane or book a hotel room down there. Orange Beach can be very crowded and commercial.
I remember some radials because our turbofan planes have no automation. We went to England last June, by the way. Send me an e-mail for info on downtown Memphis/Overton Square restaurants or outdoor recreation etc, or airport/FBO info ("2005 Edition"). Have fun!