OP: how many people do you want around you during your Spring Break trip?
If you don't want people, at all, anywhere near you, just miles of trails and desert, then may I suggest Big Bend Ranch State Park. It's 20-ish miles of caliche road just to get to the park HQ, and once you get in the park it's entirely possible that you and the missus will be the only people for 5 miles an any direction. It's BYOE, but quite a few of the campsites have a pit toilet. Also bring a truck or SUV, preferably, 4x4, and make sure you have a spare tire or two.
It may be chilly there in March, especially at night. But that'd be the case anywhere in W. Texas. Mid-May is the best time to go IMO. the weather is good, you're not quite at the point of wishing for the sweet release of death to take you from the afternoon heat, and the cactus flowers are blooming