Telling people that you're traveling around The Middle East always evokes a wide variety of responses. It's a region of the world that's not always fairly portrayed by the media. Yet, I love the Middle East and hope to see of it as much as possible. Certain countries are fairly wealthy thus not making it a cheap getaway.
Flying Pegasus, a low cost Turkish airline, was the cheapest way there from Europe. First stop was Dubai! Fortunately there are a few reasonably priced hostels that are centrally located. We paid $16 a night to be on the 66th floor and over looking the beach.
Some beaches require a fee to be paid or they're connected to your hotel. If where you are staying doesn't have a beach, ask where are the closest public (FREE) beaches.
Another cool area to visit is The Creek where you can take a boat ride to the Spice and Gold Souk. The metro and trams make the city easy to navigate but be sure to allow yourself enough time to arrive at your destination. Dubai has many malls, all pumping the AC to keep you cool on those hot days. The malls also have numerous American shops and restaurants and a heap of activities to keep you busy.
Visiting Burj Khalifa is expensive. Dubai mall is located right next door and puts on an amazing fountain show. It's better to go right before or after sunset to truly enjoy it. Standing inside the Apple store gives you the perfect vantage point.
In Abu Dhabi we only had time to visit the Sheikh Zayed Mosque. Words can't properly describe its beauty; this mosque leaves you breathless. Be sure to dress appropriately or you will be given appropriate attire to wear.