First of: There are not cheap places to stay in Dubai. That time is long gone.
So the best he will be able to do is to find a "relative" economic place in Deira, which is the area where Al Khor Street is located. I don't know really much about that area myself, but I know of a place called Gold Plaza Hotel which is right at the entrance to the Gold Souk, ie quite close to Al Khor street. I have no idea whether it is a good hotel or not, but their rates are comparatively low, ie around 50 USD a night.