Which city to visit in Europe during January?

Istanbul is far enough to the south to have decent daylight in January. You won't lack things to do in four days.

Or Athens — think of it as a chance to visit it off-season.

Go south: Seville or even Gilbraltar. If islands are allowed, why not Valletta?

Well since you ruled out my favourite winter city in Europe (Paris) I will have to recommend another.

San Sebastián (Donostia) in is a place I have only been to in the off season when the tourists were gone and I became instantly addicted.

I found it to be 100% authentic with nobody apparently behaving differently "for the tourists", just living their typical Basque lives. If you haven't spent time in Basque Country before this is a great place to sample it. I never event went to a museum because I so enjoyed just strolling around soaking up the atmosphere and hearing people speak their unique ancient language.

I also enjoyed the several other Basque cities I visited but this is the only place in the world where I tried to leave every day for over a week, checking out of my hostel and going for one last stroll, then coming back every evening and asking for "one more night please"!

Kyiv can be very charming in Winter. Otherwise go to Brussels, that's always a good choice.

What about Prague? It's a nice city to visit, there's things to see and do and the winters aren't as cold as in some of the cities you listed. There's definitely enough sightseeing to fill 3-4 days, I won't list all the sights here. Prague in winter is usually just cold, there's rarely any blizzard or bad weather as such; the city functions normally during winter too.

For indoor/evening activities, there are plenty of galleries (eg. DOX is an interesting gallery of contemporary art) and museums to go around; many jazz and blues clubs (eg. Jazz Dock, U Malého Glena) or you could just go to one of the many, many bars/restaurants.

If you like scenic views, good food, very nice people, very beautiful gardens, traditional culture / museums than I would advise Funchal (Madeira). The temperature in winter is very nice and you can get very nice prices at this time of year.

Since it's one of the most southern cities in Europe, even in winter, you can expect to have daylight until later.

Almost all activities that you can do in Spring / Summer are available now, so in general you won't be missing anything and you will get great prices.

Funchal is nice, but rent a car and travel through the island. You will be amazed with the diverse and strong scenic views.

Don't forget to go to Pico do Areeiro, Curral de Freiras (curious fact: though being an island with a max. diameter of 60Km there were people born here that never saw the sea), Serra de Agua (drink the original and famous "poncha" here), Camara de Lobos (try the Nikita drink here), the Market in Funchal, Cabo Girão, and so many other places...

If you like walking there are amazing paths.

Take a look at these images

and these