The short version
You can do Christmas in New York without ever going above Chambers Street. We're on John Street, and in December everything we send guests to is a walk: the Seaport tree, two ice rinks, the light show inside the Oculus, and a cobblestone block of bars that gets very festive around the second weekend of the month.
The honest pitch for doing it down here is crowd size. Midtown in December is a shuffle. Downtown in December is a neighborhood that empties out at 6pm on weekdays and fills up with families on weekends, so you can actually see the tree you walked over to see. If Rockefeller Center is on your list anyway, go, but do it on a weekday morning and come back down here for the evening.
One planning note before the list. Dates and prices for holiday programming get confirmed in November each year, so treat the specifics below as last season's numbers and check the venue before you go. The tree, the rinks and the Oculus lights come back every year. The exact opening night moves.
What we'd do with one December evening
Walk east on Fulton to the Seaport, see the tree, get a drink or dinner at Pier 17, then walk back up Fulton and cut through the Oculus on the way home so you catch the lights. That's about two hours at a slow pace, all of it outdoors except the last ten minutes, which is the part your hands will appreciate. Our rooftop is a nice spot afterwards if you want a quieter end to the night.
If you're here with kids, flip it: skate first in the afternoon while there's daylight, eat early, and be back inside before the temperature drops with the sun.