Is December 25th (Christmas Day) a good day to day trip to Salzburg?

Cities can't "shut down". Stores will be closed, some museums may be closed, some restaurants may be closed, while others do a booming business on the 25th. Churches may have multiple services that day. If you are planning on taking a tour, they should already have posted if they are touring that day or not.

Thank you for your reply. I apologize for confusing you with my question.

I was hoping to get a reply from someone who has visited Salzburg on Christmas Day and could comment on what sights and locations were open.

No apology is needed. :-)
Christmas in Germany and Austria is just very different than in the US and most cities are the same in this regard with typical closings and openings. This is why it is good to check websites. Many museums may trade closings each year, this year closed on Christmas, but open on New Years and next year they may do the opposite.

The 24th is the big celebration and pretty much everything is closed, including almost every restaurant. If you are in Munich on this date, you might want to find a nice hotel to have Christmas eve dinner. Make reservations now.

Christmas is a family day, meant for strolling around, perhaps a hike, view the store windows, go to a concert, have a nice dinner in a restaurant.

Some Christmas markets may be open, but not many of them as most of them close on the 22nd or 23rd. Each city is different. In Munich, Tollwood is open and that might be fun and interesting.

We took the Sound of Music tour

The Sound of Music tour on Christmas Day? Do you remember what tour company? What year were you in Salzburg?

Thanks,
Judy B

Their Christmas Market will be open.

http://www.christkindlmarkt.co.at/english/

We were there in 2011. Panorama Tours