I think you need guidebooks to study. What do you like to do? What to you want to see?
Then consult the websites of places that sound interesting and find out if they are open. Many places operate short opening hours or have sights that are closed for the season in early January.
London closes down completely on Christmas Day.
I would go to Paris or ???? first week, London is shut 25th and much wont be open 26th either.
Look at flying into Paris, Eurostar to London, London to ?????, fly ?????? to home
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