Village Divers in the East Village is where I did mine. I was satisfied, though I think I probably could have gotten the gear cheaper than I did at that dive shop. I really liked that they let you do the pool session as many times as you want until you are 100% comfortable with all of the skills. if you get 100% certified here, you will need to do the drysuit and nitrox as well. That isn't necessary if you do you open water in the carribbean.
Did mine at Long Island Scuba last year, very friendly and helpful shop; nice warm heated pool and the check out dives were included if you did them with the class.
Just about, you will need to provide your own mask, snorkel and fins for the class; after that it's the rental charge for your gear to do the checkout dives.
Got my open water cert at LIS. Get a class with Dee. He's a trip. I think that the rental came to like $80 and expect to spend around $150-200 on the mask, fins and snorkel unless you get the really cheap stuff. I bought my wetsuit there too.