Personally, I would get off at columbus circle, walk over toward the Temple, check out the Lincoln Center, then wander back toward the park. A little ways up is Strawberry Fields, and John and Yoko's apartment is right there.

My suggestion is to check this out, http://www.centralparknyc.org/things-to-see-and-do/ and then figure out which subway stop puts you nearby.

Bethesda Terrace is a great spot, and you will recognize it from about 10 million movies, but that website is helpful.

I don't live in NYC, but I love it and find myself there on business on a regular basis. I always try to leave myself 4-5 hours to be a tourist. Somebody that lives in NYC might have better suggestions, but I think you could spend your entire life uncovering different things in NYC.

A suggestion: If the weather is rainy, Central Park isn't as enjoyable, so be open to going up the east side to the Met/Guggenheim.