You have two options.
1. Go to the Souq.

2. There is small Kiosk at Villagio close to the Virgin MegaStore that have some coffee mugs, keychains, Mats, Tshirt and more souvenirs... the same articles you can get it in the City Center in one store, I cant remember the name but if you are in the level of Carrefour get the Stairs that go to the Cinema. in the First level is the big store at the left. They sale, Samsonites and Swarosky.

Also if you are in the main entrance of the City Center take a left and there is a small kiosk that have camel bone boxes... quite expensive but traditional hand made souvenirs...

I hope this information work for you.

ahhh there is a third option cheap t-shirts inside carre four!!!