3.5 weeks in Germany (and Amsterdam and Austria!)

You could easily occupy yourselves in Berlin's museums for much, much longer than four nights (which will give you only three relatively-not-jetlagged days.

I have one suggestion of a place to stay that I found amazing. It's not that far from Nuremburg. It's Würzburg. The fort on the hill is in fantastic shape as it survived 99% in tact from World War 2. Small and very charming good for a day or two.

Just one of my favorite spots from visiting Germany in 2018.

Mark

Although we stay 3 or 4 nights in a city, this still seems like a lot of check-in, check-out, find station, find hotel etc. I don't like Munich that much, but maybe you have a reason for 4 nights. 2 nights are not enough for Vienna, especially with your interests. Take some time from the shorter stops. Unless you love Mozart, maybe skip Salzburg in the winter?

Having spent time in both Cologne and Dusseldorf, I lean towards staying in Cologne, especially in the winter, because there are so many superb museums in Cologne. However, it's largely a "walking city" (normally a plus!) , which will be harder in winter. Dusseldorf has nicer older buildings (Cologne was bombed flat), but Cologne has many Roman ruins, and even a medieval mikveh, so it's not without old things. Dusseldorf may have a slight edge on food, and on contemporary art (vs. older art.)

You could use the Search box top center for more Christmas Market suggestions.

I agree with the suggestions to add more time to Vienna. Regarding Berllin, if you enjoy impressionist art, please make the trip to Postdam to visit Museum Barberini.

My thought on looking at your proposed itinerary, is that it includes a string of big cities, and no smaller places or scenic countrysides. I'd consider the middle Rhine valley, Black Forest, Bodensee and the German alps, as being worthy of visiting (and staying), over some of the cities. Just my opinion, but after a while, cities all sort of look alike to me - churches, department stores, museums, and restaurants. But I have never been to Berlin, Hamburg, or Dusseldorf, so dont know what they're like.

I'd be reluctant to stay in some of the places stan mentions in the month of December. But stan makes a good point about the current German destinations - these are all very large cities that were largely destroyed in WW II and rebuilt.

Would you have any interest in places that were more minorly impacted in the war or that still give you a peek at old-world Germany?

Bamberg (near Nuremberg) and Regensburg (not so far from Nuremberg or Munich) have been designated World Heritage Sites by UNESCO for their well-preserved medieval center.

Heidelberg and Wiesbaden also fared well in the war. Other somewhat smaller and less-targeted towns still show off their 4-500-year-old buildings these days. Many of them belong to the "German Half-timbered Road" organization and are accessible by train. They are spread out from north to south across much of Germany. Hannoversch Münden is a place I visited years ago by train, one with some 700 half-timbered buildings The Franconian group of towns (Nuremberg area on the map at first link below) might be convenient day trips from Bamberg or from Nuremberg:

https://www.deutsche-fachwerkstrasse.de/en/Homepage.html

The Franconian town names are listed at this page:
https://www.deutsche-fachwerkstrasse.de/Regionalstrecken_Staedte/Franken.html

I would agree Cologne over Düsseldorf. I would otherwise say that while each of these places can easily fill more days than you have--you won't be short on things to see and do.

As for markets, Lübeck is WAY better than Hamburg (and as Hamburg's biggest champion, that's quite a big thing for me to say). But since you already included it, you should have a really great market experience built into your trip. You could also visit Bremen, which has a fantastic market and old town.

The food will vary widely across this itinerary, so that should be fun. In Düsseldorf, the Japanese food is a bit of a must; Düsseldorf has a sizeable and active Japanese community, so you can get surprisingly authentic Japanese food. The city is sort of known for it. Hamburg is known for, among other things, seafood. The wurst is more the Munich / Nürnberg part of your trip.

Consider where you will spend New Years and how that might affect your choices.