The park offers rides, an incline railroad and a petting zoo. The summer time is considered the busy season. Another option is to ride the Royal Gorge Railroad into the canyon for a different view of the canyon (looking up). You can drink wine on the train while watching daring rafters conquer the Arkansas River. The railroad twists through the canyon and travels under the bridge. This railroad is a separate attraction from the park but I would highly recommend trying both attractions as they are so close to one another. See below for pictures and information.
Royal Gorge Bridge and Park:
Royal Gorge Railroad: