I can recommend the YHA Hostel in Dubai, about a 40dhms.($11.00) cab fare from the airport. They charged me, as a non member, 95dhms per night. It's clean and handy for the bus (no 3) to town.
I also stayed at the Anatalia Hotel, near the gold souk and close to the ferry across the creek.Do not get off the lift on the 3rd floor, as this is where the 'girlie' action happens.
For 200dhms a night, friendly staff and cleanish rooms, I thought it the best deal in the area.
For excellent food and juices, head across the creek to the Basta Art Cafe, close to Dubai Museum and old quarter. Lunch in the lovely courtyard is to be treasured.

Happy Trail - D.R.