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I can't believe I forgot to post this in my other response. I paddle at the Orchard Beach / Pelham Bay Park put-in regularly. It is used almost daily by single sculls and rowing crews, and is a great place for rowers.
In fact, the lagoon was dredged to function as the venue for Olympic Trials in 1964. There's still a viewing tower at the south end of the lagoon, by the finish line. Single scullers row down from the NY Athletic Club which has a dock about 2 clicks north, also from Glen Island which also has a shell-friendly dock. The interior waterway extends north to Titus Millpond in New Rochelle.
On Thursday I saw 2 osprey (one with a fish), a red-tailed hawk, 20-30 great egret, a great blue heron, many ducks and a couple of sea birds I didn't recognize diving for fish, not to mention a few turtles and some horseshoe crabs --- not bad for the city.
Google map these coordinates for the put-in: 40.872199,-73.797297
Parking is $7, but worth it, it's safe and there's almost never anyone parked by the launch.
Now, you need to keep in mind that buying some crappy 100 dollar inflatable kayak will not fulfill your needs. If you want to actually use a decent one, then i recommend looking into an advanced elements one. These are made of material that is very strong so they can withstand a beating. Just read some inflatable kayak reviews then you should be good to go. A price range of 500-700 can get you a solid inflatable kayak.