Fifth Avenue! Especially Tiffany & Co. Unfortunately, Fortunoff is long gone.
The Museum of Natural History and the Metropolitan Museum of Art are two of my favorites. Also check out the Frick Collection at 70th and 5th. A lovely collection, but small enough that you can go through it in a couple of hours and not get "museumed out".
Rockefeller Center is also a good place to visit. You won't get to see all the Christmas decorations, but you also won't get trampled - once the tree is lit, it's a zoo.