Not too noisy.
Not too pricey.
Anywhere in Manhattan, but below 14th would be especially good.
I don't think you're going to have a lot of options, especially downtown. Most places that are open are only doing dinner. Does it have to be brunch? Can it be lunch?
Maialino is open 10AM-2:30PM for brunch on 12/25. Reserve soon as it appears they don't have a lot of slots on OpenTable right now.
Balthazar will be open on Christmas Day but I'm not sure if it's brunch AND dinner, or just dinner. You'll need to call and ask.
The NoMad will be open but maybe more than you wish to pay.
Kitchenette and Bowery Diner also appear to be open.
Having done both Kitchenette and Essex for Christmas Day brunches in the past, I'd say they're both just okay, with Kitchentte having the slight edge, and still nothing we considered going back to the following Christmas.
They're both pretty boozy, but with Kitchenette we had a choice to order the bottomless mimosa, or not. Essex includes 3 drinks, and it's cash only. The food tasted like the kitchen staff was worn out, and rushing. You can get similar at a lot of diners.
Noise wise, Essex is deafening, and Kitchenette was so quiet it was uncomfortable talking at all.
I haven't been to most of those, but it's my impression that, for instance, Balthazar is very noisy indeed.
I was leafing through Zagat just for brunch, but haven't yet checked to see what's open. Something like Little Owl would probably be happily quiet, but it's so small that even if it's open, it's likely booked.
Just looking around OT I see Wallse, Jeanne and Gaston, Bistro La Promenade, The Standard Grill, Markt