I would go without a car.
Any official NYC cab ride to anywhere in Manhattan will cost you $40 from JFK. Going back to it, I want to say there's a $40 flat rate from inside the city, but I can't quite remember. Driving in the City is a very scary experience, even from the back of a Cab, and even from the eyes of a So Cal driver (and I know we can be terrifying at times, but oh man, that was intense!).
You could also use the Subway system from the airport and back. Once you get a little used to the subway, you'll feel extra comfortable with it after a few times. But DON'T use it late at night!
Once you're in the city, any walk is like nothing. Everything is within walking distance (especially since the blocks feel so short, and there's so much to look at you'll forget how long you've walked).
Most rooms in Manhattan are expensive. It's just how it is. Avoid any hotel immediately within or near Times Square, as they'll be the msot expensive you'll find. Don't go too far out, but really, Times Square is a ginormous tourist trap, and gets EXTREMELY crowded during the holidays. As does the rest of the City, but Times Square, and anything that features a "Classic New York Christmas" will be overpriced and crowded (TS, Bloomie's, Macy's, skating at Rockefeller Center, horse drawn carriage rides in Central Park etc.)
ETA: I really don't mean it to sound negative, hte whole NYC in the holidays, honestly it's one of my favorite times I've gone. i just want to make sure you're prepared for the crowds and the reality of the prices you'll meet once you're there
She declined.
