Coney Island is the best for everything - the beach, the rides, the beer - but mostly for the Skee Ball. It's incredibly addicting, affordable and satisfying (depending on your aim).
You've heard about the reading room at the New York Public Library, haven't you? Then I need not go on. Just look at it. And you're allowed to hang around in there!
Joseph Leonard is one of my favorite cozy spots for brunch on the weekend. After a long week of work their avocado toast and a bloody mary hits the spot. Get there early or expect to wait, it's small and limited seating. Their sister restaurant Jeffreys Grocery across the street is also very good, but no expresso drinks which and I need my morning latte.
Daytime café, nighttime bar. Nothing stronger than 30-proof. Delicious beer and really good wine. Kind people run & staff the place. The garden in the Summer is perfect. I make near-daily visits.