I go to New York almost every November or December and the crowds will be heavy. But it is so fun it doesn't matter! Just be prepared for a variety of weather. A year or two ago it was so warm I only needed a light jacket but one year it was so cold I couldn't find enough layers! Bring a scarf, hat, and gloves and an umbrella.
Also- the Radio City Christmas show usually has discount tickets available. I don't know the dates of your trip but the tickets are often at the TKTS booth and Playbill.com and the New York Times usually have discounts for them later in the year. If you want to buy them now, you'll get better seats but pay full price. Plus, if you want to see the show at a peak time, you might have a hard time finding a discount.
There is usually a Christmas shop at Rockefeller Center and Macy's has a great Holiday Lane. We like to go and buy a special ornament to commemorate our Christmas trip. Have a great time!