An old-school Upper West Side institution (especially now that H&H is gone). Foodie families will be in heaven browsing gourmet goodies from around the globe, both exotic (caviar, all kinds of cheeses) and familiar (bagel with a schmear). If you ask nicely, the man behind the smoked fish counter will likely give your kid a free taste, and there are often free samples.
Riverside Park also has many Destination Playgrounds, like Hippo, Elephant, River Run Playground and Dinosaur Playgrounds. In warmer months, the Riverside Park South extension and Pier I host lots of annual family-friendly events like Mamapalooza in May and the West Side County Fair in September.
Where the charming stringed puppets are the stars. Admittedly, it ain't Broadway, but with insanely cheap ticket prices ($5 for children, $8 for adults), short shows and post-performance sessions when kids can meet a puppeteer, it's a great choice for first-time theatergoers.
The New York Historical Society has the family-friendly attraction: DiMenna Children’s History Museum. It's a fun, interactive way for kids to explore New York City and its history, including stations that allow visitors to cast election votes and deliver a presidential address.
In addition to its seemingly never-ending Dora and Diego exhibit, the museum has some really amazing programming, especially on weekends. You can catch concerts by local kids' bands or participate in hands-on workshops with arts professionals. These activities are free with museum admission, and you can find the full schedule on CMOM's website.
The Discovery Room encourages hands-on exploration of everything the institution covers, from anthropology to zoology. Kids can build a life-size dinosaur skeleton, romp in an interactive tree house, play memory games with fossils and much more. It's very engaging for children ages 5-12, and gives parents a bit of a break (there is seating but you need to supervise your kids at all times).