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).
For the first time in Manhattan we lived on 14th street – this nice and cozy café around the corner (on 16th) still is our favorite place for delicious breakfast or brunch... Think they have tons of meals on their menu, quite affordable for huge portions.. Plus, good music.
Beach approachable by public transportation and can be connected with a visit of MOMA PS1 Art Installation (Katharina Grosse House) Also less crowed than other beaches in NYC.