I've taken each of my sons to see STOMP in NYC's East Village when they were about 9 and they've LOVED it.
A few weeks ago I posted about bringing my 9 year old to NYC and another poster recommended Serendipity 3. We went and it was great. I would recommend!
Serendipity 3 is just a few blocks away from the tram that takes you to Roosevelt Island. It's just a few dollars for the ride (you use the same card that you do for the Subway) and just kind of a neat experience if you have time.
A few years ago when I took my other son, we went to the Tenement Museum, which is also excellent. It's very close to the China Town and Little Italy sections, if you were interested in seeing ether of those. It is also within walking distance of Economy Candy, which I preferred over Dylan's Candy Bar (Dylan's is more touristy...Economy is a bit more "gritty" and not as flashy, more "bare bones" but still an excellent selection of candy.)
If you need a quick, relatively inexpensive (fast food) meal, I recommend Schnippers. They have a few locations throughout the city and their milkshakes are fabulous. Oh, I get a heart attack just thinking about the (very unhealthy!) meal I had there, but yum...
But really, I think the thing my 9 year old loved the most was climbing all over those huge rocks in Central Park. He literally just wanted to spend hours doing that.
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