Like many places in the world, Christmas is a very festive time in Madrid, but Christmas Eve itself is generally very quiet. Shops close earlier than usual (6:00 pm) and even the metro shuts early that evening...or at least it used to (Can anyone confirm?). Between nine and twelve in the evening almost everyone who can be at home is at home celebrating Noche Buena with family. Restaurants, bars and cafés are shut and the city comes to a near standstill.
Obviously hotels will accommodate their guests with a nice Christmas dinner, but don't expect the capital to be particularly lively. In fact, it will be a lot less lively than most days.
Still, with the Christmas lights in the streets, everything looks nice. You can even visit one street where they decided to hang up random lighted words. It's very unusual and very controversial because no one really knows why the City has done it or what it's supposed to mean!
Years ago, Madrid would have been shut down all night and all the next day, but nowadays you can find more and more bars opening up after midnight.
Midnight mass is held at most churches too. You can try the Cathedral La Almudena, La Iglesia de Jesus de Medinaceli, or San Manuel y San Benito (Two names, but one church). They're nice, but you will probably be surprised how solemn Christmas masses can be in Spain. At least, that's the impression I get. Considering how expressive the Spanish can be, they seem surprisingly reserved on such a joyous day. Would anyone agree?
There are other things to do, but it kind of depends on exactly what you're looking for, the age of your daughter, etc. Remember Christmas festivities tend to get started later than in the U.S. but they go on longer, all the way until January 6th.
Hope this gives you a little idea. Does anyone have any more to add?