Cordray Drug Store is an Ice Cream Shop in Galveston. Plan your road trip to Cordray Drug Store in TX with Roadtrippers.shley and Michael Cordray, stars of the Magnolia Network’s “Restoring Galveston” TV show, have opened the Cordray Drug Store ice cream shop at 39th Street and Avenue L in Galveston.Ashley and Michael Cordray draw on the butcher paper lining the tables at their ice cream shop, Cordray Drug Store.