There are several sandy areas around the park that have tiki style huts - just roofs on them, open on all 4 sides.
There is one spot that my DH and I always use, but I can't share it with the world, otherwise, we'll never be able to sit there again!
But you have to look for the sandy areas that are away from the wave pool - outside of the lazy river loop.
There are several of these areas with the hut/roofs, and eeyore0062 was right, they are usually near the different eating places. If you go during off season, check out the areas near the eating places that are closed while you're there - usually plenty of shade, and not a lot of people.
Good luck!!