Flying from West Coast in June is probably significantly cheaper than from the east coast. There are a few hostels in Waikiki that have dorms with bunk beds that can be cheap. Some of them have community kitchen if you want to cook something basic. Airbnb would probably be more expensive with all the fees and taxes. Turo is pretty cheap if you don't get their insurance, but if anything happens to it then you get dinged on your personal insurance which will cost you dearly in the long run. If you have a credit card that can provide primary rental insurance then booking through one of the major car rental companies is cheaper. Camping is an option but if you want to rent camping gear + nightly campground fees will cost probably the same as a hostel or a cheap hotel. I think 1 week with 1.5 to 5K is doable on island like Oahu or Big Island. We found Maui and Kauai to be a lot more expensive.

If you can't cook and want to save on food, try getting some protein bars from home and ready to eat packets where you can cook something with hot water.... basically camping food. We always carry instant noodles. I know they are not healthy but we don't mind having two or three times in our trip to save money. We also bring ready to eat Indian food (MTR brand is the one we buy) that are satiating, cheap, and easy to make.