Picnic near the park is easy. Balducci's has a location on 66th, just west of Broadway. That's upscale, so if you want a regular grocery store, Food Emprium is at 68th and Broadway. The even easier option is that It's a Wrap (69th and Broadway) delivers to people in the park. ALl of these things are right outside an entrance to the park, at 67th and Central Park West, which itself is right outside the Sheep's Meadow - a HUGE field perfect for what you're planning. Take the 1 train to 66th street to get to this stuff. The Central Park Zoo is a fantastic idea - very kid oriented.
Toys R Us is famous for having a ferris wheel inside. Not sure if that was mentioned before.
If you go to Coney Island, there's an aquarium there. To an adult's eyes it's a little run-down. Kids might find it cool.
Regarding the 11th, in past years things have not shut down. However, many places offer a moment of silence. Just remember that a lot of people will be thinking about that day.
There's the Sony Wonder Technology Lab at 56th and Madison. It's neat and has hands on stuff, but I don't know if a 3 year old would appreciate it for very long.
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Cogito ergo spud -- I think, therefore I yam
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