Galveston Island State Park stretches from the beach to the bay, 10 miles west of the city of Galveston. Most come to the state park for the wide, sandy beach on the Gulf of Mexico, and then stay to camp at either the beach side campground or the bay side campground.
NOTE: The park was damaged by Hurricane Ike two years ago, but has recovered quite well - the facilities are still not completely back to where they were, but restrooms and showers are now available within the park.
There are 4 miles of hiking and biking trails within the park on the bay side.
The State of Texas has also established several paddling trails for canoes and kayaks on the bay side, the Dana Cove trail, the Oak Bayou trail, and the Jenkins Bayou trail. The best description of these paddling trails is on the Galveston Island Paddling Trails web site.
The state park has an excellent, color, trail map of the hiking/biking trails and the paddling trails, but it does not appear to be online yet. The map we link to here has the trails on it, but it's not as clear. Ask for the paper map at the park headquarters.
All year.