I'm in NYC as well, and am curious what flat water you're talking about. The Hudson and East River may appear flat, but both are deceptive - they are tidal estuaries and can range from placid to really scary. They have a lot of boat traffic, from jet skis to cabin cruisers to high-speed ferries to large tug-barge combos.
Also, I'm learning that a lot of the reservoirs and lakes in the NY/NJ in the area do not allow inflatables. Even the NY Water Trail put-in at Orchard Beach in the Bronx does not allow inflatables. I'm not sure if this applies to the other Water Trail put-ins.
When I first started out, I took some lessons at the kayak company at Chelsea Piers - there's also the NY Kayak Co at Pier 10. In addition to the suggestions above, it's a good idea to get some local knowledge.
Hardshell Kayak Sail Rigs
PFD's (Life Jackets)
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