The Alex Gibson shipwreck is the remains of a wooden barge. The barge was built in 1877 was 180 ft long and displaced 2154 tons. She was sunk in the 1930s and now sits in 40 ft of water on a clean sand bottom.
The Alexander Hamilton was the last of the steam-powered side-wheel riverboats of the Hudson River Day Line. Built in 1924, she ceased operations in 1971. A well-meaning group pulled the Hamilton from the mud in 1977 and moved her to a temporary berth along the east side of the Navy pier, planning to restore her as a museum. Unfortunately, at the new more-exposed location, the old vessel was sunk and reduced to scrap by a sudden storm in November of that year. The last records indicate that the wreck is still there, and you can even make out the outline on Google Earth.
Once you get there, suit up at your car and walk down the small stretch of beach till you get near the jetty. Enter the water at your leisure. Once in the water, you can swim north along the jetty to the tip. You may see fish, lobster, crabs and the sort. There are large openings in the rocks that form the jetty. Large enough in fact that you can almost swim into one. I don't advise doing this because getting stuck might be a frightening experience.