This list is for my cousin's, Keith and Sammie. They are headed to NYC for their 10 year Anniversary in a couple of weeks, and here's some of my favorite things to do (most involve food) that are a little off the beaten path (I figure Times Square, Rockefeller Center, Empire State Building are things you're already planning on doing).
Ferry to Staten Island: One of the best deals in NYC, this free ferry takes you to Staten Island and back. The view is
Metropolitan Museum of Art: I hear the admission is 20 dollars now, but the Met is still worth it. Take the Best of tour, it's free with the price of admission, and the tour guide gives you a tour of their favorite pieces in the museum rather than a preset tour. The pieces you see give a great introduction and overview of a grand ol' museum. Then go see what you're interested in--you'll probably have already seen at least the Egypt room in Movies. Great view of Central park, and one of the coolest Museum rooms I've ever seen.
Greenwich: Dunar Kebabs, Magnolia Bakery banana pudding, pizza by the slice, etc etc. Greenwich is great to just walk through, but I always find myself eating my way through. The funky shops, the people watching, it's a great place to spend a few hours. I almost find myself a little disoriented in Greenwich, but don't worry-it's small. You'll figure it out. Lower East Village is another great place to eat your way through.
My favorite Subway stop: This is a silly one, but I really like 72nd and Broadway a lot. The subway station is picturesque as is the neighborhood. There's a Grey's Papayas (ht dogs done right--and cheap, ask either of my brothers about these) across the street, several places to eat.
5th Avenue: If it's a hot afternoon, and Keith is willing-going into Tiffany's, FAO Schwarz etc. Both are worth just seeing, and ask prices on the rings. You'll be amazed-at least I was.
One More: If you're going to Palmyra, go see Niagara Falls. Crazy tourist trap, but still impressive. I like the view from both the American and Canadian Side, and find both to pretty developed. Canada is fun to spend a few hours in however. I didn't do the boat ride as it was closed, but did pay on the Canadian side to walk down to where you're right next to the falls.
New York is a cash mostly town.
Bring comfortable shoes.
Public Transportation is fun, walking is one of my favorite things to do in this city.
I'm sure you know the tips to get the cheaper Broadway tickets.
Yes, the Subway is dirty, and don't look at the tracks too long, but it's easy, pretty cheap, and you'll have a good time figuring it out.
Also, if you can-go see either the Mets or Yankees play. Baseball games in NYC are a TON of fun...even if you're casual fans.
If anyone else wants to give Keith and Sammie any suggestions, please feel free!