I grew up in the West Eighties in Manhattan in the 50's and 60's. We lived in the museums in the neighborhood, especially on rainy days. Good thing no one told us how much we were learning!
To echo some thoughts above, do not miss the Natural History Museum, The New-York Historical Society (the carriages collection is great, but the whole place is a pure simple delight, and of course, the must see Metropolitan Museum of Art on the other side of Central Park. Set aside at least three days for the museums - your trip will be memorable and 'non-touristy.'
I have known people in past years who stayed at the little gem called Leo House. Couldn't say enough good things about it. Keep your pocketbook in front and do not stare up at the tall buildings as you walk along. I envy you your trip. Have a safe and fun one.
