Galveston Island State Park has two parts. There is the sea/beach and on the other side of the road you can visit the nature center and walk through the wetlands.
After the nature center there were many signs saying that there were alligators in the park. I doubted it a little, but we did the "alligator loop" a little hike around some sweet water pools. Suddenly we heard a big splash nearby! A big alligator got in the water. Not even a minute later this one came from the opposite direction. He swam quickly towards us. I took a few photos and then we walked on, especially because we had Baloo with us!