Between Christmas and New Year’s.

What are you interested in? History? Art? Churches?

Are there any kids in the family of six? Ages?

I don't know your preferences, but Franz Joseph who ruled the Austro-Hungarian Empire for much of the 19th Century really spent a lot of money collecting everything that wasn't tied down by others in the Middle East and it is all at the Kunsthistorisches Museum. (It is good to be the emperor!) Good range of art too.

https://www.khm.at/en

And hit a concert - there will be lots.

@NickB

Any concert venues you would recommend or places to look for concerts?

A family of six may have wide musical tastes. Vienna has a continuous parade of music venues and opportunities.

Vienna State Opera

https://www.wiener-staatsoper.at/en/

Or consolidator sites like:

https://www.viennaconcerts.com/

or

https://www.visitingvienna.com/entertainment/christmas-concert-listings/