I and my 2 daughters will be arriving in Salzburg by noon on Christmas Eve, and will be in Salzburg for all of Christmas day. Beyond having made dinner reservations for Christmas night at St Peter's Stiftskeller, I don't have a game plan, beyond our own walking tour.

I realize that, given the holiday, much will be closed, or will close early. We would love to attend some type of concert or theater event. Any recommendations are appreciated, as are ideas for things to do on Christmas day.

The easiest and most comprehensive tool to find out what will be going on in Salzburg is the event calender of Salzburg's TI website:
http://www.salzburg.info/en/art_culture/events_calendar
You'll find many cultural events like concerts on Dec 25, the Christmas Market is open, and even when you are not into religious "events" you could think about visiting the Christmas Eve/late night or Dec 25 morning service at St Peter's Cathedral. Should be quite festive..

Have a look to the music calendars of the Cathedral and Franziskaner Kirche. Sunday and festivities High Masses at these two churches (9am Franziskaner, 10am Cathedral) usually have choir and orchestra.

We did the sound of music tour on Christmas

Bigtyke... I was considering that tour, as it only seemed to last 4 hours and covered a lot. Did you enjoy it?

Yes, My family enjoyed it (third time for me, second for wife) it covers mainly the places outside the city. Many of the in city locations are in pedestrian only areas, or areas awkward for the buses to visit.

If you can make it after your dinner the "midnight" service at the cathedral is very special. I think you ave to line up about 9:30 to get a seat (it will be packed). The music with a formal choir and orchestra plus a quartet with guitar doing silent night is very special. That could be the highlight of your trip.