Between Late December to Mid January - London, Paris, Italy or other

It's busy that time of year up until the 2nd week of January and everything except church is closed Xmas and New Year's Day.
If you happen to choose London on Xmas Day, there is no public transportation running except taxis or private ride shares. The weather is better in Italy than Paris or London that time of year.

If I was in the UK for Christmas I would choose Edinburgh, where there is good public transportation, even on Christmas Day. As a result the city is not as dead as most of the UK is on that day.

Welcome to the Forum!

Do you want warmer weather?

Not sure where you live as your profile doesn't reveal that so not sure if you are looking for a cold Christmas experience or warmer, possibly sunnier weather.

What date in December are you looking at arriving?

I, personally, would go for London (in spite of transit issues and would stay in a hotel where this mitigated it somewhat) or Paris but I'd be looking for cool Christmas lights and displays. I've always wanted to go to the Christmas at Kew Gardens (right outside London) display and see the decorations in stores this time of year. With Paris there is apparently a cool light display at the Jardin des Plantes and I've been there in late Fall when the street decorations were going up which was neat.

I've been to all three of these places during this time of year.

This past holiday season, I was in London (Dec 17 to 23) and Paris (Dec 23 to 30). Weather is iffy in either place. It will be cold and probably wet. A lot of your activities will be indoors. If I had to choose between the two, I would go with London. Even though both cities were crowded this time of year, I felt like there was more breathing room in London. Also, there are so many interesting (and free!) museums. Others have mentioned that London public transit shuts down on Christmas, which is why we went to Paris for 12/25. This is something to consider when booking hotels and making plans.

Where do you want to go in Italy? I was there in the 2013/2014 holiday season. We stayed in Rome, Florence, and Venice. The weather was chilly but definitely warmer than London and Paris. I wasn't there on Christmas, so I can't comment.

Thank you so much for the suggestion.

I see the OP has edited to add their dates. With 3 weeks to enjoy, there's no reason why they couldn't split their time and do 3 or even 4 cities. 5 days each in Rome and/or Florence or Venice, plus Paris and London. But if OP just meant a shorter visit within that time range, I'd pick London. We were lucky enough to spend time in London over Christmas and New Years a few years ago. And we had made arrangements to deal with the holiday closures. We even had a white Christmas, which made strolling through the parks on Christmas day extra special. And I got to experience the Boxing Day sale at Selfridges first hand, lol.

@CJean, that experience is awesome! One of my highlights of many London visits over the years was snow at Christmas 1981 in London. I was living in FL at the time so any snow was cool but snow in London topped it!

And thanks for pointing out the changes in the original post with the update on possible travel dates and OP's location.

So, Tanya, if you are from sunny Texas you might want a vacation where you can experience winter, lol!