Where to go in Europe in Dec or Jan ??

Italy or Spain because they have mild winters and beauty, comfort, ambiance and a places of happiness, good food, of moderate budget, and museums.

I've been to Innsbruck skiing in February, and it was incredibly beautiful from the top of the ski slopes. But the slopes were steep and icy--with marginal new snow (vs. our beloved Lake Tahoe.)

But we just about froze our tails off in Venice on that trip, and they had wooden sidewalks on St. Marks Square because of high tides. Winter weather in Italy is cold
But if you must go to Europe in winter, you just have to accept that the weather is very cold and variable. The best weather you may find is in the Algarve region in Portugal flying into Faro from England..
We usually wait until the last few days of March to go to Europe as the winter weather has usually just broken about then. And the Spring airfares usually go up about that time.

We have been to England, Scotland and Austria in the winter. All were lovely. The Christmas markets in December make Austria a great winter vacation place. Vienna has several. Innsbruck's is smallish but very nice. Our favorite is Salzburg. It is one of our favorite destinations anyway, but in December it is especially nice. It snowed a small bit while we were there and temps were around 25 -35 F. But we had good coats, gloves and hubby wore a ball cap and I wore a hooded scarf and my coat had a hood, too. When you get chilled, you can get warm spiced wine at the markets, or stop into a café for hot chocolate, coffee or tea. With the marvelous pastries, you really have a treat. And Austrian food is great for winter- goulash, great soups, roast pork, wiener schnitzel, noodles, etc.

Edinburgh and Inverness Scotland are great in the winter, too , as is Aviemore, in the Cairngorm Mountains of Scotland. Edinburgh has smallish Christmas market, too. But the absence of large crowds of tourists, helps make these places really nice.

London, York and Bath all are nice in winter and all have Christmas markets (Bath's is especially large with many high quality craftsmen). There are plenty of day trips you can do from London, too, which makes it a great place to base yourself.

One 'drawback' some will mention is the short day. Sunrise may not happen until 8 or 9 ish in the mornings and sunset will be around 3ish in the afternoon. But that was not a problem for us. Especially in the big cities, there are plenty of indoor activities, plus, we weren't there to take lots of photos. We wanted to go to museums, see plays, shop, and enjoy good food and drink.

We were not in northern Italy where Venice is located.
We went to Rome Siena and Orvieto December 28 2016 - January 5 2017 and it was at least 50 degrees and no rain each day

We were in Rome Florence and Venice in February 2002 and it was in the lower 50's each day.

Either embrace the cold.
Budapest > Vienna > Prague > Berlin

Or avoid the cold,
and head to Spain or southern Italy.

We were in Florence last year during the end of November. Loved that there were no crowds and that we could walk right into the museums. Took several easy daytrips to Siena, Lucca and Fiesole.

How long a break are you planning?

If places close at any time of year, it will be in January, so you will have more flexibility in December. I was in Venice last January and many restaurants were closed for a few weeks.

The German Christmas markets in December are interesting, but the food there isn't generally the best in Europe.

Budapest was good when I was there in December, but cold and very foggy for a couple of days. The major cities such as Paris, London, Amsterdam and Rome have things to offer all year round.

If you want countryside, the answer is similar to the places recommended for other times of year, such as Scotland, Switzerland (expensive), Scandanavia for the fjords, Granada and the White Villages of Andalucia, Holland for the canals and Ireland.

I know this is a European forum, but many Europeans head to Morocco, where the weather should be better and there is a great mix of scenery, coastline and cities such as Marrakesh plus a different culture.

Our favorite time in Venice is December. Dec 8 is the kick-off of the Christmas season and the lights are great, crowds are non-existent. Also loved London in winter, as well as Rome and Florence. An itinerary with outdoor activity possibilities coupled with museum for inclement weather is ideal.

I see you're from the Bay Area, so I don't know your cold tolerance, but Scandinavia really does have excellent price cuts during the colder months. My airfare was $750 total from O'Hare to Arlanda to Kastrup back to O'Hare in mid-November. Temps were 30s to 40s, which is like spring for this Midwestern gal. Plus, there was a huge snowstorm in Stockholm hours before I landed so it made it even more beautiful!

Almost any big city in Europe is worth going to in the winter, as long as you dress properly. There will always be museums and other indoor things to do, and the streets will be as beautiful as ever (except for the lack of flowers). We've been to Budapest, Vienna, Strasbourg, Munich, and Salzburg in the winter, and loved all of them. On the other hand, the countryside and smaller towns can be less interesting, unless of course it's a ski area.

I've been in mainland Greece in late November/early December and it was fabulous. Mild weather and no crowds. Outside of Athens you practically have museums and sites to yourself. But many hotels and restaurants close for their own vacations, so do plan ahead. And museum/site hours will be more limited.

Sunlight was extremely limited. The sun went down at 4:00 pm every day, but the temperatures didn't drop too much.

Than hou to all that submitted suggestions.
Looks like Europe will be wonderful at any season.
The planning begins...