Both Waipio valley and Pololu valley would be great. Large camping areas and plenty of trees to hang. Waimanu is great too if you're prepared for the extra hour or two of hiking (past Waipio) to get there. Be prepared for rainy weather though in any of those spots - especially in the winter.
The western (Kona) side is much, much drier and more consistent weather wise as it only gets about 10 inches of rain a year. Beaches are better for swimming too if that matters to you.
Hapuna Beach - as someone mentioned- is a great beach but not sure how many hanging options you'd have. It's technically a public beach, but connected to a resort so even if you found a good overhanging tree they might not like you setting up there. Also, if you're planning on staying overnight you'll have to either sneak in or just arrive before 6pm and hang out (guards will stop you if you arrive at night and aren't staying at hotel). Mauna Kea beach just down the way is similar to Hapuna with same situation.
I'd check out 69's or Makalawena Beach. 69's has plenty of good trees on the beach, and Makalawena has some good trees a little removed from the beach. Pretty reliable dry weather too and no hassle from Hotel security.