Go shopping in the Village, stop into Mario Batali's Otto for a fresh pizza, enjoy the electricity of the city. I'll also put in an enthusiastic second for Central Park! Central Park Zoo, the Carousel, Shakespeare Garden, cocktails at the Boathouse for Mom & Dad...you could really spend an entire day in the park, and did on many occasions when we lived there.
Honestly, in all the time we lived in the city with kids, there wasn't a single occasion when we wanted to go to Mars 2012, Jekel & Hyde, or any of those touristy spots. I'll never really understand why people suggest these places. As far as I'm concerned, if you can find a colorful, gimmicky flyer for it in the rest stops as you head north on the NJ Turnpike, I'd consider skipping it altogether.
As to World of Disney, well, I lived in Manhattan for years before I decided to give it a look and was completely underwhelmed. There's so much to do and see in the city, please don't make a special trip for it.
I'd also consider either going online or to your local Barnes & Noble and purchasing a copy of Time Out NY or Time Out NY with Kids. It's the best resource for finding the most current events going on in the city during the exact dates you'll be there.
Have fun!!