There are many car rental offices in Jiddah,I have noticed that most of them are located at Madina Road,heading south.
some are international chains like AVIS rent a car,or it could be some local place.
As I have described earlier it is extremely cheap and convenient to rent a car in Jeddah keeping in mind you have proper documentation available with you. Gasoline in Saudi Arabia is less than a dollar a gallon. There is also ample parking through out the city and to top it off most of it is free. You must have a valid International License as well as traffic checks are quite frequent and you might not want to spend some time in the Saudi Jails.