One of my favorite dependable winter haunts is along Vulture Peak Road in Wickenburg, AZ.
Pure desert, tons of sand, and most if it along a series of washes, with epic landscapes of desert shrubbery and the iconic Vulture Peak rising above.
Technically not *totally* free... this area is actually State Trust Land, which requires a $20 permit for limited camping throughout the year with permit displayed.
It's fairly convenient to town at the "usual average distance" of roughly 7.5 miles to downtown Wickenburg with it's small assortment of fun western shops, cafes, small movie theater, grocery, and fast food. There's also a Safeway within 4 miles on the way back to town at the corner of Vulture Mine Road.
The AT&T coverage isn't particularly good at camp... sporadic at best, and non-existent at worst. There is SOME type of tower overlooking camp however, so if it's yours, you might be in luck.