We would like to take a three-day weekend and visit Europe over the Xmas holidays. Where would be a good city that doesn't completely shut down for those three days? Thanks

We have been to Bruges and Strasbourg and enjoyed both for their xmas markets and lights.

Belgium and France are good choices because neither has 26 December as a public holiday. In France, the 26th this year should be much like any other Saturday, with shops open. In most European countries, there is public transport on Christmas Day. Britain is about the only country where everything shuts down at Christmas (Ireland is probably the same but I don't know as I haven't spent Christmas there).

Amsterdam is open over Christmas both 25th and 26th - at least most of the museums are, and public transport runs as normal.
The shops will be open on 26th too.
The only problem may be finding somewhere to eat on the 25th but even that is probably possible, and you could always book somewhere ahead of time.

Rome, but it's expensive and if you want to do anything you need to get tickets now.

Avoid Germany during the Christmas holidays.