Legally, you can't get a long term lease without an RP. Your RP, depending on the company, will take at least a few weeks from your arrival. My advice would be to get somewhere short term, a serviced option, whilst you wait. This will also give you a chance to look around and find a place to live that you actually like.

Short term options - Mirageproperty.com (selection of fully furnished short term options in a few different central areas...good quality)
Ezdan Suites - Most popular short term option. Quality is not great, but has decent facilities. Good for a couple of weeks.
Retaj Hotel and Suites - Few options around town.

Hope that helps!