NYC is one of the most fun places to be in, and there are so many cool things you can do without spending a lot of money.
central park is always an amazing experience, also, in the summer, there are a lot of free music and theater events, like the river to river festival.
China town is one of my favorite places, and there are a lot of cool Chinese restaurants there that are cheap and really yummy. Just walking around is really fun.
When I have visitors of all ages from out of town, this is my favorite thing to do - take the F train across the water to Brooklyn bridge park, then cross the bridge on foot, with a great view of the statue of liberty, Alice island and the Manhattan skyline, then walk through through city hall area and on to Chinatown or SoHo - it's impressive, fun and doesn't cost at all...
Also, there's always the apple store where you can listen to lectures about computer (I like the one in SoHo for that) and play around with gadgets.
And, MoMa have a free admission every Friday afternoon, The Metropolitan museum of art is pay upon donation (so though they ask for 20$ you can actually go in paying only 1$) and the Brooklyn museum is free every first Friday in the month.
Oh, and Meccaran park pool, in Williamsburg got free movies and parties on some of the evening os August.
Have fun!