I've actually spent the last couple months researching the different opportunities in and around NYC and my conclusion was that, just like boats themselves, each place has it's tradeoffs. In my case I was looking for a place to improve my skills, learn racing and an environment where I could enjoy ongoing sailing opportunities. After spending a lot of time looking into different places, I realized that there was a couple key criterea for me: i) cost; ii) convenience; iii) sailing conditions; and, iv) ongoing sailing opportunities.
Location quickly became a big deal. I don't know if you just want lessons, or whether you are also looking for a place to continue sailing throughout the season. Since I wanted a place to continue sailing, location quickly became a big deal. I checked out most of the places listed above, partly to get a feel for how far they were and quickly starting ruling several places out. I was impressed with the two places that Caleb mentiones, SailNY and New York Sailing Center on City Island. I also looked at the Offshore Sailing School which runs a program out of Chelsea Piers.
Offshore Sailing School probably had the most professional educational program and was convenient, but there was no ongoing sailing opportunities as far as i could tell and it was pricey.
SailNY has a racing program that goes through the winter which was appealing (i think) and it was also the cheapest. Downside for me was that it was in Jersey and I thought I would use the onging sailing opportunities less as a result.
The New York Sailing Center on City Island had an interesting offer which was that if you sign up for several classes, you got comped on the first year of club dues (which were the second cheapest I found). The fleet seemed great and the guy who runs it was clearly very knowledgeable (believe he was the son of the guy who first started it) and enthusiastic. Another nice thing was that you could take the boats out with crew that were not part of the club, whereas many of the other places restrict your ability to do that. Wasn't much in the way of facilities, but I figured who cares as it's all about the sailing. I also liked the place for sailing as you didn't have the same currents and boat traffic that you get on the Hudson and Harbor, plus it's reasonably sheltered so you don't get the seas you would get out at Sheepshead Bay area (lots of places out there - too far for me). The seasoned Sound sailors cautioned me about light winds in the summer though. This was ultimately my second choice, but I ended up passing for the same reason I passed on SailNY which was the convenience factor.
Ultimately, I settled on Manhattan Yacht Club. The lessons seemed pretty competitive with the other programs, but were more convenient to get to (starting nevigation class next tuesday). They have racing on Tuesday, Wendesday and Saturday nights in the summer and one of my goals is to learn to race so that worked. It's the most expensive of the bunch dues wise, but I figured I'd use it twice as much as it's basically on my way home from work - so I rationalized that the per sail cost would be less! Of course, there will be the currents and boat wakes in the harbor, but as I said, these places all have tradeoffs.
I'll be curious to see what you find/decide on. Hope this helps