New York
That far downtown is mainly a business district. It gets quiet at night. South street seaport is nearby. Its a tourist trap, but has some cool stuf. You will be right near battery park which has the ferries to liberty and ellis islands. From the world financial center dock, which is right there, you can take a boat to Sandy Hook NJ, which has a huge nude beach. The walk along up along the Hudson from there is nice and its all now part of a new state park.
The best thing to do in NYC is just walk around and see what you encounter. There are all sorts of neat neighborhoods, shops, restaurants, parks, and so on. Also just about every subway stops over there so you can get anywhere quickly.
Also if you want to do something that is clothing optional there is always Robert Moses "Lighthouse" beach. A very friendly and safe place for some fun and frolic in the sun. Enjoy NY it has quite a lot to offer and after your first visit you will want to return for more of that N Y attitude. Don't forget about a visit to us here on Long Island with the Hamptons, North Shore Wineriers, Antiquing, Hiking, Boating, quaint towns and friendly villages.
Buy a weekly subway ticket - it will save time and can be used on the busses! Investigate the "New York City Pass" for faster entry into some attractions, e.g. MOMA and the Empire State Building. Look out for farmers' markets, there is one on Union Square on Saturday mornings.