If your plan is to buy name brand items at a nice Phan Rang mall, you may need to wait about ten years. As of now, not lot of modern retail outlets nor specialty shops designed for tourists exist. A few electronics stores can be found at the city center. For souvenirs the best selection is at Po Klong Garai where a large open air building contains many shops carrying Cham trinkets and other locally made products. The Saigon-Ninh Chu Hotel also has a gift shop.
The local markets don't attract too many tourists and venders focus on providing the locals with food and household goods. However, you are in luck if you want to see local seafood just off the boat. Go to the small fishing villages near the center of Ninh Chu Bay and follow your nose.
The best alternative for casual and beach clothing and the only shop that targets overseas visitors. This small shop sits at the intersection of the beach road Yen Ninh, and the main street connecting it to Phan Rang.