Cool - good luck with the move.
I'm sure many others will chime in with ideas. I would recommend hopping off I-10 near Las Cruces, NM to check out the white sands monument, VLA, and Ruidoso/Cloudcroft. Nice areas to explore and very unique.
Texas hill country is also interesting to ride around. Not the greatest road conditions but if you haven't explored Texas much it would definitely be worthwhile. San Antonio is well worth a visit if you want to venture that far south. Southern Louisiana would also be quite interesting...
Lastly, you are going to have some very beautiful riding just North of you. Northern Georgia, TN, and WNC are all amazing places to ride, but since you'll be living so close to all that now I'd focus more on the southern option rather than heading all the way up to I-40, you'll be able to do all those others easily after the move. Just my $.02