Oh, man, thank your dad for taking you, what a great trip!
Specifics depend a lot on your interests, but here are some things I would do.
Get a half dozen at the Grand Central Oyster Bar. Sit at the counter and if you don’t know what to order just tell the guy “I don’t know what to order, what’s good?” He’ll set you up.
And Grand Central is worth a look-see regardless
Ride the subway, it’s the fastest way around unless you’re close enough to walk. Get the $8.25 1-Day Fun Pass
If the weather’s nice, people will be out in droves in the park.
Here’s Bethesda Plaza in October
The NY Public Library Main Branch
Fifth Avenue at 42nd Street
Intrepid Sea-Air-Space Museum
http://www.intrepidmuseum.org/
American Museum of Natural History
Central Park West at 79th Street
http://www.amnh.org/
If you see a Gray’s or Papaya King, get a hot dog & papaya juice
If you see a hot dog cart, get a hot dog
That’s just off the top of my head. The possibilities are endless. Have a GREAT time!!