How much time in Salzburg?

The problem is time of year. I can't advise as to Budapest, but Salzburg and Prague are going to be pretty slow this year with Christmas falling in the middle of the week. Sundays are normally days when only minimal services are available, Mondays are not much better. Christmas is Wednesday, and with Christmas Eve on Tuesday I would expect things to close up early and stay closed until Thursday, and that only gives you 3 days in the entire trip when things will be open as "normal".

Salzburg is an ideal city for taking things slow, Prague is also. I can easy spend 3-4 days in each just walking around and eating and drinking as the mood hits.

I like to stay in boutique hotels (Domus Balthatzar in Prague and Boutique Hotel am Dom in Salzburg) but you may want to try the bigger chain places just to ensure you have services over the holidays.

All of Budapest, Prague and Krakow have much lovely architecture to look at on days when everything is pretty much closed. I feel as if I did a lot more walking in Budapest (which is the largest) to see those pretty buildings; public transportation was there to be used, but my preference is to walk most of the time. I believe you can see more in a condensed area of Prague, and of course Krakow is the smallest by a considerable margin.

Unfortunately, the weather may not be so great for strolling outdoors. The historical averages cutting off in 2000 included in the cities' Wikipedia articles show that Krakow is likely to be the chilliest and Budapest the warmest, but the differences are not great. In addition, the Krakow article includes averages for a more recent period that are warmer; perhaps December/January has warmed up in the other two cities as well. You're considerably more likely to face precipitation in Krakow, and it will have only about half as much sun as the others (an average of about 1 hour per day vs. 2 hours).

We spent 3 1/2 days in Salzburg and feel it was about the right amount of time. The better part of a day was spent at Schloss Hellbrunn but the garden and "trick fountains" tour wouldn't apply in December. Another big chunk of time was spent at Hohensalzburg Fortress and yet another big chunk of time was spent at the DomQuartier museum complex. If you have a car, Hohenwerfen Castle in Werfen, Austria (filming location of Where Eagles Dare) might also be worthy - especially if you're a film buff (we also found the Leonardo Da Vinci museum entertaining).

We arrived in Budapest on Christmas Eve and stayed for several nights a few years ago. I think you would find enough to do there. We had a nice Christmas Eve Dinner, went to the Christmas Market and took a boat cruise on Christmas day, and saw the Nutcracker Ballet and went to the Baths on the day after Christmas. By the 27th, thing were re-opening. One more day would have been nice. We spent several more days and new years eve in Vienna before flying home on New Year's Day.

So I don't know Prague, but Budapest was fun.

I thought three nights was enough in Salzburg in summer. In winter, your suggested two is probably good.