I don't know of any hostels in Dubai. $80/ night seems pretty cheap for a Dubai hotel. What is your budget, when are you staying, what are your minimum requirements for a room, and how far away are you willing to stay?

Dubai is expensive. Hotel rooms in the New Dubai area tend to go for around $300+/ night. Old Dubai is (somewhat) cheaper, but (much) more confusing if you are driving. Sharjah and Ajman should be a lot cheaper, but even I can't figure my way around those places, and I live here!

If you are staying for awhile, sometimes you can rent a room in someone's house (look on some of the expat sites). But they usually want someone who is staying for a couple of weeks (and preferably a month).