in the Hawaiian islands Budget Accommodations are there for the finding. Hawaii is very friendly towards retires so there is allot of budget accommadtions. Your best bets are to look out to the outer islands Maui Kauai & the Big Island of Hawaii in particular have the best deals for long term budget accomodations.
If you are looking for budget hotels Accommadations then you best bets will still be on the neighbor Hawaiian islands rather than Oahu. however Oahu and Waikiki still have some great Hawaii accommadations . you can also still find long stay stuff around the island take H3 and make a left at the bottom of the hill.