Been there, done them.
Petra by night is worth it, but take headlamps, as the Sig is quite dark. Light tripod is worth taking along also (if allowed), I did not have one but did get a passable 2 sec exposure by using an information tablet as support. It is an amazing place, I spent 2 days there, also walking the upper trails which are quite deserted. The light chances during the day quite a lot, so you are likely to shoot same spots twice as they will look different. The "Monastery" is also well worth the climb.
I took the standard "beduin camp" trip to Wadi Rum, which was ok, but after that I hired a private 4x4 which took me to the southern parts near the Saudi border. It is restricted area and I am not quite sure if it was legal or not, but the scenery there was even more amazing and no other vehicles or tourists in sight at all. The wind carved cliffs are unreal and one could easily spend days there to shoot abstracts of changing light.
One handheld panorama looking over to Saudi Arabia (clumsy stitching, just for fun):