I know it'll be hard to believe, but my family (5) did a trip to New York City for a little under five hundred dollars. (Okay fine. We stayed in my sister's condo so that was a big money-saver, but still!)
We drove from Chicago, ate mostly sandwiches on the way out and back, and stayed for three days. Our first night, we went to Chinatown. Good shopping, good food, and very very cheap prices. Then we saw an off-broadway show. It was pretty good, and much less expensive than broadway.
I'm trying to recall everything we did. I know we went to SoHo and window-shopped, went to Greenwich Villiage, walked down Fifth Avenue, saw Times Square and Rockefeller Center (Spl?). We went to the large Nintendo Store (for my son) and the wonderful New York
Disney Store (for us all! We spent a LONG time in there.)
So all those places took an entire day, and they were all free. Just a little light shopping cost. We walked all around, and finally took a taxi for about six dollars back to the train station.
We went to Ellis Island and the Statue of Liberty another day. I believe it was less than a hundred for all of us to go. That was terrific. We had a great time, AND you could stay at each place as long as you wanted.
The museums were wonderful too. Metropolitan Museum of Art, National Museum of the American Indian, and the Museum of Natural History. (We cut through Central Park and picnicked there.) The museums, I believe, were all "free", but a suggested donation was encouraged. Give whatever you feel comfortable.
By scrimping on meals while traveling, we could splurge a bit more while actually in New York City. Window-shopping let us experience a lot of New York City without paying a dime. And the museums definitely don't drain your budget.
Good luck!