Grand Central, Hudson River Park, The Highline, and Prospect Park go without saying.
There are a few other major ones I have not been to, but plan to: Van Cortlandt, Pelham Bay, Inwood Hill, Shirley Chisholm, Jacob Riis, Freshkills, etc.
These parks are somewhat rundown but have great potential if they were better funded.
Notes: The area around the lake floods constantly and has extremely few bathrooms. It's more fun during the summer when it's dry and you can watch 10s of soccer games going on, tons of cricket games too. Do the fountains at the Unisphere or the Fountain of the Planets ever work?
Notes: I guess it's a part of Flushing Meadow Corona Park. Similar to FMCP, it does not seem to get enough love (funding).
Notes: Overrated and unfortunately feels slightly rundown. Still nice to visit during the day but would be great if they could remove or replace all the broken light fixtures throughout the park.