May and June are great times to see ospreys (Pandion haliaetus), those wonderful seaside raptors that love to dive into water to catch fish and nest high in trees or on platforms. I have seen ospreys at Marine Park (Brooklyn), Jamaica Bay Wildlife Refuge and Broad Channel Park (Queens), and Mount Loretto and Great Kills (Staten Island). They nest in May, and by June have little ospreys sticking their heads out of the nest. In July and August, you can see the youngsters learning to fish, and see them keeping their eyes on their parents in case there is food to be had. There have been osprey flyovers at Central Park, but I've never seen one land there. They have a very distinctive flight, which you can see in the video below.
This Filming the Feathers video was shot at a nest at Marine Park, two nests at Jamaica Bay and another nest at Broad Channel Park. Music is by Giuseppe Maria Cambini, Wind Quintets Nos. 1, 2 and 3, performed by Soni Ventorum Wind Quintet (obtained from MusOpen.org, a royalty-free music source). One of the nests at Jamaica Bay Wildlife Refuge has two babies, which you'll see sticking their heads up and flapping their little wings.
The first osprey I saw was at Marine Park in July 2015. I didn't venture out to see others until May and June 2017.