A place for a week in December

I know it's kind of close to Vienna (in a way), and to many people somewhat similar to Vienna, but I love Munich. It is a happy city, IMO. Lots to enjoy in the city and beautiful scenery in the environs. Not to mention the food! And before Christmas there will be lots to put you in a holiday mood. An overnight trip to Rothenburg will fit in as well. As for science, the Deutsches Museum is fantastic! The Treasury at Nymphenburg Palace will wow you. The music halls are lots of fun, and just in general, I find it a place that makes you smile. I think it will give you the same satisfaction that Vienna did.
Check out comments on the Germany forum for further suggestions. I have wonderful memories of our visit there.

It's a common answer to many questions of this type, but IMO for good reason: London.

In addition to London which is a good recommendation, and Vienna where you’ve been, my favorite big cities for a week are:
Paris
Rome
Istanbul
Madrid
Or for less jet lag, better December weather, good value, and most of what you want (food, art, culture, history ) Mexico City.

I suggest Mainz. Close to Frankfurt so you can do the markets there. Also within an hours train ride you have Wiesbaden, Heidelberg, Koblenz (with the really fun Winter Garden), Neustadt, Rudesheim, and Speyer. A little further out there's Trier, Koln, and Wurzburg. The river cruises are mostly shut down, and the Rhine valley towns are mostly closed up, but there's a lot of other stuff to see and do. Take your son to the Technical Museum in Speyer! Hit the Art Museum in Frankfurt! Check out the Temple of Isis and the Roman Amphitheater in Mainz! Go to Deidesheim and eat at one of the multiple Michelin starred places!

As a Munich native, I could now say Munich :-) But honestly, I'm more inclined to go further south.

My personal winter travel destinations in the south are Lake Garda (although a lot of things are closed there, which is what makes it so attractive to me) and Lake Como. Aside from the city of Como, many of the smaller villages are probably shut down as well. So, in my case, Venice would be my choice.

In your case it sounds a lot like Budapest or Paris to me.

We loved it — the markets, the public transit, the music, the time
spent just being in one place and going deeper and slower.

We are all into good food, sites, science, history, music. I like
doses of art. We all like exposure to other cultures.

• the time spent just being in one place and going deeper and slower. https://youtu.be/1nd5AtZIrTk?feature=shared AND https://youtu.be/0nd9DuDGCz0?si=aa0c19KaJHEtabkX AND WINTER https://wheretogoin.net/best-things-to-do-in-budapest-in-winter/
• Food https://community.ricksteves.com/travel-forum/hungary/restaurants-in-budapest-revisited
• Science https://kozlekedesimuzeum.hu/en/institutions
• History https://budacastlebudapest.com/budapest-history-museum/
• cultures, unique in Europe: https://hungarygoldenvisa.io/guides/hungary-culture-and-traditions/
• the markets https://community.ricksteves.com/travel-forum/hungary/the-christmas-markets-open-soon-in-budapest
• the public transit https://welovebudapest.com/en/toplist/2024/08/12/how-to-get-around-budapest-a-guide-to-public-transport/
• the music https://community.ricksteves.com/travel-forum/austria/music-venues-in-prague-budapest-and-vienna
• Hotels https://community.ricksteves.com/travel-forum/hungary/rs-forum-favorite-hotels-and-their-cost

Definitely London. And even though he's 17, you might want to consider the London Zoo. When our daughter was a freshman in college, we went to London in Dec and she suggested the zoo. It's a really good one, with some reptiles we haven't seen in American zoos.

London for sure. Love their style of Christmas Markets. One thing to remember is London is every expensive a value city would be Munich.