The Met is awesome, MoMa is great for modern art and The Frick is a brilliant collection of pieces from the old masters.
Walking the Highline is really nice on a nice day. Stop by the Gansevoort/meatpacking area afterwards too. Lots of cool shops and you can stop by Rapha for a coffee.
Walk the Brookyln bridge and explore Dumbo.
Smorgsaburg is a sweet outdoor food market in Williamsburg, though it might not have started up in April.
The Staten Island ferry is free and a good way to see the Statue of Liberty.
If you like pickles stop by The Pickle Guys. If you like movies then Katz does a great pastrami sandwich (not cheap though) and you’ll recognize it from the film.
For eating check out the roof top restaurant in Eataly. Great views, great beer and great food. For drinking there’s so many great bars and pubs. My favourites are the Pony Bar in the Upper East Side (American Craft beer bar) and Valhalla in Hells Kitchen (Again, lots of craft beer, though not just American). Top of the Strand in the evening for sweet views or there’s the Bar Downstairs on 42nd and 5th for posh cocktails 🙂