Hawaii has never been the place to go if you have a tight budget. Right now however if you ever were planning to go to Waikiki Hawaii is a great time as the current economic sitatation has many of the Waikiki cheaper hotels lowering there prices as the low end of the market is the most affected so Go To Waikiki and fun! The local saying is that "nobody ever said paradise is cheap" Waikiki cheap guesthouses and budget accomodations are either hostels or what would be a budget hotel elsewhere with really high room rates compared to most other tourist locations.
Finding the best Waikiki cheap hotels however is not that hard Waikiki Outriggers hotels seem to almost always have internet specials going on with the exception of the peak season around Christmas. The Outrigger Reef while still in the final stages of a major overhaul is a great example and one of my favorite hotels anywhere. You get a ocean front property with a very nice pool, great restaurants notably the Shore Bird and bars and shopping on this mini resort. Many travel agents will have the Outriggers and have package deals. Generally the lower the rate the further from the beach but all Waikiki cheap hotels & guesthouses are walking distance with the exception of the UH Hostel listed below. For the most part you will not really need a rental car once you get to the hotel schedule your car trips for the begriming or end of the holiday in Waikiki and walk the rest of the time. there are car rental places very close to all the hotels in Waikiki book a ride with the hotel shuttles to or from the airport.
Waikiki guesthouses & bed and breakfasts are non existent there are several waikiki hostels that for the budget trawlers are what you will probably end up staying at. Some, many of the Waikiki Hostels are very noisy with parties, others are more subdued. Generally my suggestion would be to stay at Waikiki Hostelling International if you are going to be there for a while, the UH location is the place to stay with its garden settings also it is cheaper as you are not paying Waikiki rates for everything. I am not sure but they use to have a location up on the east side of the island that you might want to to check out as well if you really want to get a feel for the real Hawaii.