Basically the town of Broome goes from 15000 people in the wet to 30000 people in the dry. Organise your accommodation before you get here otherwise you will be paying $130 a week for a piece of grass and the need to buy camping equipment.
Unique Suggestions: If you do "turn up" go to the Broome Visitors Centre near Male Park in the centre of town and ask there.
Fun Alternatives: Sleeping in your car might be the best option just do not get caught by the rangers or cops. Most people do book well in advance especially around Broome Cup time (horseraces)
When we went to hire a car it ended up costing loads more than the advertised price we had looked up on the net before we left.
Part of it was our fault because we had looked during 'off season' when the advertised price for a small car was $40au a day. When we hired it was 'shoulder season' and the price had gone up to $58 a day. We really wanted it so went ahead anyway, then after most of the paperwork was done fond it was another $20 for insurance and a milage excess, so it ended up over $80au
Fun Alternatives: If you're staying within Broome, don't bother with the hire car, use the buses and taxis. Almost all the day trips out will offer a courtesy pickup from your accomodation.
If you want to drive around and see the outlying places get a 4WD (will cost twice a much as the small car)