Well it all depends on his interests and the time of year.

Circle Line has a fun fast boat around Manhattan, my dd liked it and took some of her friends when they were 17-18.
Circle Line New York around Manhattan sightseeing tours

You can get "student rush" tickets that are generally around $25 if you show student id's (and usually you can get 2 tickets).
This is a message board where they discuss which shows give this:
All That Chat

I love street fairs! They are free, they close the entire street for several blocks and are filled with ethnic things for sale and lots of fun foods to eat. They are so much fun and a real taste of NYC. For a listing:
SCHEDULE New York City Street Fairs and Festivals
here is another link, sometimes they don't list all on each site:
NYC Street Fairs - Festivals 2008 - NYC - New York City

If he is going this summer, Bryant Park offers free Broadway concert snippets:
Bryant Park | Calendar

John's Pizzaria in Times Square is fun to eat (it is located inside a converted church with a giant stained glass ceiling).
John's Pizzeria - Times Square - New York, NY, 10036-3900 - Citysearch

But if he is going in the winter, there is inexpensive skating at Wollman Rink in Central Park, or Bryant Park is even cheaper, and way cheaper than Rockefeller Plaza.

Down by WTC if you continue down you can take the Staten Island Ferry for free.
"From the deck of the ferry you will have a perfect view of The Statue of Liberty and Ellis Island. You'll see the skyscrapers and bridges of Lower Manhattan receding as you pull away and coming into focus again as you return."
I took teens on that and it was a nice cheap and fun ride and we rode back and then continued on with other sites in the city.
Staten Island Ferry Information

Then there is the fun of chinatown. I just love walking around and checking out the interesting shops.

There is a section of the village that is Japanese. Both my dd and ds went to Japan and loved going here where almost everyone speaks Japanese and they loved the shops and the restaurants.

Then there are museums.

It is hard to suggest if I don't know your son's interests.

If he is into sports, you could always catch a game at Madison Square Garden or check out the giant Nike store uptown.

There is always Lincoln Center. In the summer they have a open air free concert series and in the Spring/Summer they have free dancing. My dd and her friends used to go for free Swingdancing.

If you post some of his interests, I could suggest some other options.

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