I'd avoid Boston. You don't have a ton of time for that. It's about a 3-4 hour ride depending on traffic.
There's a lot to do in the city. Central Park is always fun, even a small zoo in there. Plenty of shopping. Head downtown to the seaport. I'm not a big museum guy so I can't help you too much there. If you're into naval/Air Force history the intrepid is always open. Or the museum of natural history (you can spend a full day there and still not see it all...). There's always the Empire State Building, Times Square, Rockefeller center and countless other small parks.
Always plenty of shopping and eating. I kinda just try new places every time I'm in there so again sorry not much help. You can always head out to bars. The barcade is fun, they have craft beers and vintage arcade machines.
If you're willing to travel Coney Island has the amusement park and beach/boardwalk. Been a while since I was there, so it might not be the nicest after dark. Long Island also has some of the best beaches around. You can just take the LIRR out of penn station/Madison square garden. They started the buses to jones beach again. If you rent a car there's always Robert Moses. Take the train to Babylon for some more drinking/bar hopping. You have wine places like barique, dancing at Lilly's, craft beers at the villager, etc. OR head to Freeport and go down to the nautical mile. Lots of bars and restaurants on the boardwalk. Good seafood there too.