Depends on how far you are willing to go. I'd recommend areas of Arizona and Utah. We visited Bryce and Zion near that time (end of March, our spring break), and it was lovely. Zion was packed (and so was every shuttle in the park), but I think Zion is always packed. Bryce was not busy at all and was by far my favorite of the two. I've also hear good things about Canyonlands and Capitol Reef. You'd have to consider weather and how cold your camping gear goes. Same with Grand Canyon. We've camped there more than once, but both times in the summer.
It's about 2.5 hr to Zion, 4 to Bryce (by car), and 3 hr to Joshua Tree NP, also a good time to go. We've been camping in Joshua tree many many times, in Feb, March, April, May, and April (Right around easter) was the best, but again, weather varies. Could be really hot, could be really cold.