My fiancée and I are back from the Big Island. Here are some places to hang...
Pololu Valley is a short steep hike from the trail head to the beach. Up from the beach is a forested area, but no water. Didn't hang there, but wish I would have.
Waimanu from Waipi'o will kick your a$$. But well worth it. It has designated camp sites, we camped at site 9, but site 7 is better suited for hammockers. Water is available from a natural spring and from a river that empties into the sea. There is a little bit of a sea wall to prevent the river from becoming brackish. Plan on sleeping 2 nights in the valley to recover from the hike.
Halape is a very remote beach site that starts from Crater Rim Road in Volcano NP. At the time we were the only ones there and got to experience full body tanning.
All of the coconut trees are full. Water is available from the cistern at the emergency shelter. Check with the Park Rangers on how full it is before you leave. There is a brackish pool that is hidden along the coast if you're looking to cool off. There is a bunch of pre-established tent sites, the first one you come too off of the trail is the best one to hang at. I would recommend staying 2 nights minimum.
Waimanu and Halape rains at night and the wind from off the ocean can get a little strong, so pitch your rainfly low. If you tend to get cold at night, bring a pad or a fleece to sleep on top of.
Kulanaokuaiki campsite at Volcano NP, got down to the high 50s... I wish I had brought my underquilt. Hang from the trees on the big central lawn. Make sure to bring some long underwear.