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If you have two sons that you'll be traveling with, why not check to see if the Rockette's Christmas Show is playing that day at Radio City Music Hall. They had performances on Thanksgiving Day, so maybe they'd be open on Christmas as well.
I think NYC would be best on Dec. 25th. It is a large multi-cultural city, not everyone there is a Christian, so more things are open, more people are around. Though it will be quieter than usual, it won't be dead.