Christmas in Germany

10-13 days is not many. Consider that travel takes at least ½ day to get from one place to another. And if the arrival and departure days are counted in that 10-13, you have 'only' 8 -11 full days. And you have mentioned 5 possible countries. Getting the "most bang for your buck" is not best done by spreading yourself so thin. If you have 10-13 full days on the ground (arriving day 0 and leaving day 11-14), I would say you want at the least 2 days in each place (and thats full days, so three nights). So I would think about 3 places, tops. And I would make them very time efficient to travel between. Being in smaller towns usually means more travel time to and from an airport, so that adds to the travel time. And I would book an open-jaw ticket (in one city, out another).
As for where to go in Germany, or elsewhere, you need to get a few guidebooks and start reading, and considering ease and time required for travel, in addition to your interests of course. Personally I think England and Scotland should be put aside for another time. Dedicate another trip just to them. There is a common anxiety amongst first time visitors to Europe that you will never be able to go again and so you have to see everything you've ever wanted to in one trip. Assume you will return. Think depth over breadth and make the time rich and full, not stressed and busy.

Christmas markets are a big thing to visit. But many close on 23rd or 24th December (they start last weekend in November). So they will need to be planned for the start of your trip.

Lüneburg tourist info (in English!): https://www.lueneburg.info/en/english-homepage/
Info on Lüneburg Christmas market (German only): https://www.lueneburg.info/de/weihnachtsstadt-lueneburg/

If you arrive on the 21st (overnight flight taking off 20th), then your first 2-3 days should be in Lüneburg, to get acquainted with a real German town, and visit all there is to see.
BTW, Hamburg airport to Lüneburg is to be done by train, don't even think of hiring a car at the airport.

That gives you 7+ days of touring, though 25th December is best in Lüneburg as little will be open. That is enough time to do northern Germany, but not much further afield.
Hamburg is 30 minutes from Lüneburg by train, best done as one or more day trips.
Two nights in Berlin (2h50 from Lüneburg by train).
Cut south to Prague (4h by train from Berlin)
Further south to Vienna (another 4h trip)
Fly back to Hamburg, or direct home from Vienna.
If you have some more days, after Vienna go to Munich (4h20), and fly home from there, or train to Lüneburg (6h)

That is just my off-the-cuff suggestion, with the cities in order so the trips between are not too long.
You say you have never been to Europe, so you want the beginners guide to trains, it is here (start with this page, and move on to the rest of the site): https://www.seat61.com/Germany-trains.htm

Thank you for the suggestions so far. I can take Copenhagen and/or Oslo off the list. Obviously I want to see as much as possible, but also am realistic enough to know that I have limited time. I was really just trying to get a better sense of where I should prioritize my travels, and within the countries mentioned, what stands out as "must see" to those who have been there before. It may be I have to take GB off the list for now, and I do plan on going back again in the future. With it being winter, it seems like it would be best to pick spots that have abundant indoor activities, such as museums, or are small enough to be walkable in bad weather. I've got travel books on hold at the library and will use those to help plan as well. Thanks again for any and all assistance!

My daughter will be doing study abroad in Luneberg, Germany in fall.
I'd like to spend Christmas in Germany, then move over to England and
Scotland for the remainder. Yes, I know it'll be very cold and wet,
but this is the best time for us to go. So my questions are; where
would you recommend we visit in Germany? Id love to be in a smaller
town with Christmas market.

Lüneburg actually IS a smaller town with a Christmas market. One of the most beautiful near Hamburg. Even better are the Harz mountains 2,5h to the south of Hamburg however. This region offers several beautiful, preserved towns with literally thousands of half-timbered houses. Two of them, Goslar and Quedlinburg, are World Heritage Sites, but Wernigerode, Wolfenbüttel or Stolberg are just as nice. The Harz mountains also offer the biggest steam train network of the country, with one route up to Northern Germanys highest mountain, the Brocken, and interesting churches, among them one of Germanys most beautiful Gothic cathedrals, and several important Romanesque churches... some of them are actually World Heritage SItes.

The Christmas markets in Germany stop shortly before Christmas, and Christmas itself is a very quiet affair (the country more or less shuts down completely), so as a tourist you should either stay in a big city, or in a region with enough sights. The Harz mountains offer enough for a few days.

I've got travel books on hold at the library and will use those to
help plan as well.

Good look. Non- Bavaria is badly covered in some travel guides, especially American travel guides, and Rick Steves actually doesn't cover this region at all.... despite his 30+ years hunt for a second Rothenburg ob der Tauber... which he would find in Quedlinburg.

"I was really just trying to get a better sense of where I should prioritize my travels, and within the countries mentioned, what stands out as "must see" to those who have been there before"

You may have heard the the famous Q and A about photography:

Q: What's the best camera to use?
A: The one you have with you at the time you want to take the picture.

Similarly, it's not that there's anything wrong with wanting to go to Great Britain, Copenhagen, or Oslo, or that they are "better" or "worse" than Germany for visitors. It's that with 10-13 days, and the requirement that part of that time be spent in Luneberg, you will not want to waste a lot of time in transit to far-flung places, but will do better to focus on places nearby - which as you have been told, are quite rewarding in themselves.

While Rick doesn't have information about places like Quendlinberg, he does cover Hamburg and Berlin. As you say, one advantage of big cities like these is that they have lots of indoor attractions for when the weather is not conducive to outdoor activities.

Do check those Christmas market dates. Most actually close on the 22nd or 23rd, very few are open on the 24th. With the 23rd being a Sunday this year, my guess is that most will close on the 22nd. Small towns may only have them for one weekend and these are usually towards the beginning of Advent, not the end.
The 25th and 26th are holidays and all stores will be closed. Museums may or may not be open, so best is to check the individual websites. The 24th is not an official holiday, but everything pretty much shuts down by 14:00. This includes restaurants. Most museums will simply be closed that day.

Hi all,
I just want to thank everyone for their input. I have taken suggestions to heart and now the proposed itinerary is keeping us at least in one (largish) area. Our plan is Hamburg (Luneberg)> Rothenburg>Munich>Vienna>Prague>back to Hamburg to depart. We have a total of 12 days, not including travel days, so we feel this will give us a good flavor of the region while still having some quieter moments at Christmas proper. I had hoped to fit Berlin in, but that would rush us in other spaces too much.

Now...on to figuring out train travel in Germany....!

Thanks again!

Twelve days to see all those places would be rushed for me, particularly since Vienna, Prague, and Munich are large cities. Remember that two nights in a place equals one full day of sightseeing, and one night is less than a full day. You lose at least a half day, end to end, when you change cities. Also, at that time of year there will short daylight hours, so your time for walking around places and seeing things outdoors will be limited (sure they have electricity, but seeing a city by night isn't the same as by day).

For those reasons, I'd cut one place - at least.

I agree that you're still attempting to do too much (i.e. will be spending much of your time in transit and checking in and out of hotels and getting oriented). And if Christmas markets are important to you, you'll only have a couple days.

My preference would be to enjoy the market and surrounding area of Luneburg and move on to Hamburg or Berlin from the 24-26th, which are big enough cities that some things will be open (but you'll still find even the biggest museums/etc closed on Christmas, check hours of sites you want to see before you finalize your itinerary). Another option would be to go to France for Christmas, as the beautiful Alsace region has some Christmas Markets open through the New Year in Strasbourg and Colmar, or Vienna, which keeps its market open through the 26th.

What I would not want to be is stuck in a small town in Germany between the 24th and 26th. There will be little to do but take long walks.

I agree with the others about still cutting back. Prague and Venice really deserve more time than you would be able to allocate to them. Leave Munich in and if you really want to visit Austria, you could tack on Salzburg. It's touristy, yes, but it's also charming and has a lot of beautiful scenery.

All,
The itinerary is shaping up. Prague has come off the list due to budget (insanely expensive for New Years Eve, IMHO) and train travel. We did add Salzburg on our way from Munich to Vienna. I have a big question that I have searched this forum and Seat 61 for an answer, but haven't found it, and hope someone here can help.

We are considering sleeper car from Vienna to Hamburg on 1/1. Since this is obviously a holiday, can anyone confirm this arrangement will even be available? bahn.de does not have schedule that far out yet, and I need to firm up lodging ASAP as places in my price range are going fast.

Thanks for any help you can give!