Long Island Sound averages 60 ft in depth, with the greatest depth of over 300 ft at the eastern end. Tidal effects are strongest at the narrow western end, where all the inrushing water flow piles up and makes tidal variations of up to 7 ft. Strong tidal currents are also prevalent, and visibility tends to be poorer than the open ocean, especially at depth.
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.
Now, most people would look at the heading on the page and think that I was crazy for diving near a nuclear power plant. Just to calm your fears, this power plant was never brought online, so there is no chance of getting radiated at this location (barring a nuclear war while you're diving). With that said, Shoreham can be a very interesting dive. Located on the north shore of Long Island (I don't know the name of the town, look on a map), it is a shallow dive with an average depth of around 16 ft. Visibility tends to be anywhere from 3 to 10 ft.