There are local buses which goes from Aqaba/Petra/Amman to Wadi Rum very regularly....
It is the city on the shores of Mediterranean Sea. It borders Saudi Arabia on one side and Israel on the other. And if you take a boat ride in the sea 10 mins, into that one can easily see Egypt. It is famous for shopping and beaches. Temperature here in general is 5-7 degrees higher than Amman. It city has beautiful corals underneath its water one can enjoy Glass bottom ride, snorkeling, scuba diving etc.