All good suggestions ... unless you want to party. In that case:
* Go due south to Gulf Shores, Ala., and eat at Lulu's (the restaurant run by Jimmy Buffet's sister); then
* Go due west to New Orleans (staying a Bayou Signette State Park during your time in The Big Easy); then
* Continue due west to San Antonio and feast on Tex-Mex along the River Walk; then
* Take I-10 and U.S. 385 to Big Bend National Park (OK ... there's not much partying there, but the place is amazing!); then
* Go just a tad out of your way to see Carlsbad Caverns; and
* Stop in Tombstone, Ariz. (The Town Too Tough to Die and home of the newspaper with the greatest name ever, The Tombstone Epitaph); before
* Finishing in Tucson.
It isn't the shortest route, but you'll enjoy the ride (and should avoid much of that winter weather you're worrying about).