If all you want is cheap then try Golden Sands 5. I stay there when I'm there and pay 175 dirhams an night (30 pounds) for a single studio serviced appartment which even has its own fridge and cooker etc. Great because I can easily knock up an ommlette myself for breakfast.
Great location just behind the Ramada and close to the Burjuman shopping mall.
No need to be on the beach really as the taxis are cheap and plentiful.
If you do go to Dubai make sure you spend a day at Wild Wadi, it's a great day out and you can scare yourself ****less on the Jumaira Scarer
Golden Sands