Hi Shortypops,
I'm afraid I don't know of any light aircraft you could rent near Abu Dhabi and I think you'd need a foreign licence verification & validation from the local CAA in order to do so anyway.
As you asked about other areas here with GA though, we do have a flying club in Qatar and there is a very keen GA scene with light aircraft, microlights, gyrocopters, light jets etc.
You would need to obtain a local licence to fly here though.
Hope that helps.
Qatar Flying Club