If you want to do ice skating, there are a few other options besides Rockefellar Center - not necessarily as "Christmasy" but less crowded and more affordable.
The Pond at Bryant Park - free to skate, you just need to pay for skate rental (which I think is about $10) if you don't have your own. Smallish rink so it can get crowded.
Wollman Rink in Central Park - larger rink than either Rock Center or Bryant Park, don't know the pricing as I haven't been there in a few years. Not as touristy as the above two.
American Museum of Natural History - I've never been to this rink (it was new last year) so I can't really comment on it, just throwing it out there as an option.
I agree with the PPs, NYC at the holidays is wonderful. There's so much to see, beyond the normal tourist attractions. You could spend a weekend just looking at all the special holiday decorations & visiting the "destination" stores like Toys 'R Us, FAO Schwartz, American Girl Place, & World of Disney.
It will be very crowded, so don't plan too many things for one day & try not to go all over the place - for example, if there are several things you want to do in Times Square, do all of those things before moving on to another area. Sort of like planning a Disney trip, lol. It will take time to navigate through the crowds to get from place to place.