Just making sure you realize that "nature" is not necessarily contradictory with "NYC". :) For instance, if you take the subway as far north as it goes, to the northern tip of Manhattan, you'll be in the neighborhood Inwood. This is where you will find the last remaining virgin forest in Manhattan. No, I am not kidding. I haven't been there myself, but I've seen pictures. I have a friend who lives up there.

There are TONS of walking tours available in NYC. I'd try a Google search for that. I've heard of some very interesting ones that I've considered going on, but haven't yet. Another potentially fun option is the Circle Line Ferry. You can get a view of New York from the outside on a ferry that gives you an option of making a trip around the southern tip or a trip around the entire island.

There is a big airfield in Brooklyn out toward the Rockaways (don't remember the name). They might have some kind of museum or exhibit. Not sure. (Sorry to provide such an incredibly vague scrap of information.)

And, boy howdy and a half, does NYC have music, which might make Joe really happy. I'd suggest checking things like the Village Voice online to see what kinds of options you might have. And both mcroft and immlass know much more on that topic than I do.