At Mustang Island State Park, what you do is up to you. You can play at the beach (swim, surf, build a sand castle), camp, picnic, fish, hike, mountain bike, kayak, bird watch (especially during spring and fall migrations). Paddle the Mustang Island State Park Paddling Trail. The three segments of the trail follow the western shoreline of the island in Corpus Christi Bay. The 20 miles of trails pass through some of the best shallow-water fishing areas in Texas. Enjoy close-up views of coastal birds. Traditions anchor here in Port Arasnsa and Mustang Island State Park