If you would really like to "do in on the cheap" then bring a t-shirt, sun block and a bathing suit. Plan on staying at a number of beaches and parks that are free and allow overnights. I know lots of people that have done this. No tent really required. Not even a sleeping bag, just sleep on your towel.
Easiest, rent a cheap car, bring some food with you in a ice chest, and buy the parishavbles there. BBQ, swim, snorkle, watch the sunset and bring a book. That is relaxing in Hawaii on the cheap. This life still is available on Maui, Hawaii and Kauai. Most places provide water, BBQ pits and toi's. Some have miles of open beaches for camping without charge!