As a general rule, every park sees higher than usual visitation over Spring Break and summer.
Pedernales Falls State Park is a probably a good choice, as is
McKinney Falls State Park or
Bastrop State Park, though both of theses are closer to a major city (Austin) and might get more crowded. Most of the lake parks get busy but they have a lot of campsites, so you might look into
Choke Canyon State Park (but probably avoid
Inks Lake State Park as it's the most visited park in the state -- very beautiful but guaranteed to be at/over capacity.) If you'd like a higher liklihood of relaxation, you could stay at one of the more 'primitive'/less developed parks like
Colorado Bend State Park.
I don't traditionally camp during Spring Break, so I'm just basing these suggestions on relative visitation at the parks year-round. There are dozens of parks that would meet your criteria, it's just a matter of finding the one you'd like to explore this Spring Break.
Good luck!