One of the most amazing artifacts on the Galveston island is what remains of Fort San Jacinto.
The construction of the fort at the eastern tip of the island began in 1897 and was garrisonned on April 28, 1898 by Battery G, 1st U.S. Artillery. There were four batteries built. The Great Storm of 1900 badly damaged the fort and it was abandoned for a few years, until 1911 when it was repaired and re-garrissonned.

The concrete structure is what remains of Battery Croghan. The battery originally had two 15 pounder 3" Driggs-Seabury M1898 rapid fire guns. The guns were supposed to be shipped to Europe during World War I, but the war ended before they actually made it there. Eventually the guns were remounted.

The Great Storm of 1900 greatly damaged the battery along with the rest of the fort. Eventually it was rebuilt and a mine casement was added (the rectangular structure on the western side). The mine casement tunnel and the entrance to the tunnel can still be seen.
After World War II the battery was declared obsolete and was inactivated in 1946.

Many people walk the dirt road that would take you very close to GZ. However, there are no trespassing signs at the gate by the seawall. I myself prefer to stay on the safer side and I would recommend to walk the beach. The terrain might be slightly higher this way but it's beautiful!
Sources:
Fort Wiki - Fort San Jacinto
Texas State Historical Association
The rise and fall of Fort San Jacinto (The Daily News)
National Archives