On either side of the island, you notice some reinforced doors blocking entry into the mountain slopes. They seem magically sealed, and you don't see any other way in.
Because of their location and the strange machinery rusting away nearby, you determine these doors lead down to the mechanisms that help power the great wings of the island. You had a great view of the wings from the air as you approached, and they definitely weren't large enough to do any sort of flying on their own; likely, more magic was involved, and the wings simply gave forward motion to the city.