I've been to Prague and Vienna during the holidays. Loved both, but Vienna is amazing at that time of the year. How big is the family? When it is just my wife and I, we train it. It adds a nice time to relax as well.
When we travel as a family, we also normally train. Last summer we wanted to travel from Prague to Salzburg with a stop in Český Krumlov, the train schedules didn't work for our time. We wound up using Daytrip (mydaytrip.com) and also added a stop in Hallstatt. Great service and I'd use them again.
If it's not too presumptuous, a great hotel in Prague is Pod Věží (www.podvezi.com). We've stayed there 3 times in the last 2 years, it has the best location right at the end of Charles Bridge. If you want a special, not necessarily inexpensive dinner, try Hergetova Cihelna (cihelna.kampagroup.com/en/). You will need a reservation but you can dine at water level in the shadows of Charles Bridge; spectacular food and view.
I usually don't recommend chain hotels, but I wound up staying at the Hilton Vienna Plaza multiple times for work and just love it. The location is perfect as it is on the Shottenring and a short walk to large market in front of the city hall (Wiener Rathaus). While I was working in Vienna, my favorite "local" pub became the Gösser Bierklinik (www.goesser-bierklinik.at/en/). Try the Gösser Dark, ummmmm. The food is great and inexpensive. My first stop when I'm in Vienna.
Less than an hour away from Vienna is Bratislava, Slovakia. The Christmas Markets there are wonderful. Smaller than the other cities and less commercial when we visited (4-5 years ago). One of our favorites and highly recommended!