Hey Marley,
You might try Camp Mokuleia its a quiet isolated beach on Oahu's North Shore, 4 miles from Kaena Point. I'm not sure of the cost but I do believe there are no free places especially goverment land. Reservations are required; Camp Mokuleia, 68-729 Farrington Hwy., Waialua, HI 96791 tel. 808/637-6241. Or you might try working through this list which is a bit dated "2003"
http://www.alternative-hawaii.com/accom/occcp.htm