Where should we go? Where do we start research we are Europe newbies. Would like to visit Christmas outdoor markets, love art and theatre, architecture. Thinking Denmark as one stop cause my husbands family is danish. Maybe Scotland. And a couple other destinations Would like to explore rail travel options. Maybe3-4 destinations in 14 days. On a budget.
Denmark and Scotland are among the more expensive countries in Europe, but very nice to visit. I have been to Copenhagen around Christmastime and it was lovely—shop windows all decorated, lots of lights, and a festive air. This was actually in late November, so the Christmas market were not open yet.
The best way to combine Denmark and Scotland would be to fly from Copenhagen to Edinburgh. Taking the train would add considerable time and expense to your trip.
In Edinburgh you have an opportunity to see excellent theatre. You can get an idea of what is offered around Christmas time by looking at this year’s program on sites like this one:
https://www.whatsonstage.com/shows/edinburgh-theatre/
What did you have in mind when you mentioned Scotland? It is a beautiful and very friendly country, but in winter the cities would be a better choice than, say, the Highlands or islands. Glasgow is great for exploring the architecture of Charles Rennie Mackintosh—-we really enjoyed a day walking the “Mackintosh trail”, even in the rain.
https://peoplemakeglasgow.com/see-do/tours-trails/charles-rennie-mackintosh
https://www.walkhighlands.co.uk/glasgow/mackintosh-glasgow.shtml
If open to ideas other than Scotland, consider taking the train from Copenhagen into Germany, where there are any number of opportunities for visiting Christmas markets. I will leave it to others to recommend their favorites, but will note that Hamburg, Bremen, and Köln (among other possibilities) are all within easy reach by train from Copenhagen, for a start.
From western Germany it would be a short distance to Belgium or the Netherlands if you wished to include one of those countries.
If Denmark is your major destination, I would save Scotland/England/Wales for it's own trip. The land transit can be a challenge in the Winter taking 32 hrs from Edinburgh and Copenhagen. You might find a deal on flights. It would much simpler to start and stay in mainland Europe. Check package tours which cover transportation and accommodations and some meals. A friend of mine took one of the river boat tours and visited many Xmas Markets and made many new friends, besides. It is hard to estimate what all these would cost if you had to pay separately. You have a year to save up.
Try Budapest, Vienna, and Munich. Budapest excels at architecture, Vienna excels at art, and Munich gives you a sample of German markets. All have plenty to occupy you during the day, because you can’t really Christmas market all day and night.
Easy train connections and not some of the most expensive destinations. Buy multi-city airfare, flying in to one city at the beginning and out of another at the end.
But your list of great destinations could be very very long, with no bad choices.
Keep in mind that December days are very short in northern Europe, and you may not see much sunshine. Copenhagen has an average of 41 hours of sunshine in the entire month of December. The figure for Edinburgh is somewhat better at 49 hours.
Google Flights is showing a two hour, non-stop flight from Copenhagen to Edinburgh for as little as $18 on Ryanair Airlines. Carefully check what extra fees Ryanair may charge before buying tickets.
I am extremely fond of both Scotland and Austria, but with 2 weeks and Denmark and Christmas markets your main objectives, I would limit your trip to Denmark and Germany.
While almost all cities/counties have Christmas markets these days, Germany and Austria are where they started, and generally where they are done best.
If you want a UK option, I encourage you to consider London. You will have great art and theatre options and the decorations everywhere are first rate.
Don't worry about the short days. Life continues after sunset and the atmosphere is unique and beautiful.