Where to go in Europe after Aberdeen - Late Nov/early Dec?

November is cold, dark early (4-ish) and frequently wet. I would stop in Edinburgh if only because it is a great place as well as having the nearest large airport. Get a taste and move on. In December head south - maybe Paris or the south of France. The second half of your trip will overlap with Christmas Markets so you could also visit Strasburg or Munich, or many other places. It may depend most on where you are departing from in the US since you will want to end up in a place with good connections home to save vacation days for vacation.

I assume you haven't booked your flights yet.

If you want to save Edinburgh for a future trip, easyJet has a nonstop flight from Aberdeen to Paris on Mondays and Fridays. You could easily combine Paris and Alsace. Paris will be chilly, but everything will be open. And Alsace will have the Christmas Markets along with the wine villages and Strasbourg.

The discount non-stop flights from Aberdeen go to London, Paris, Amsterdam, Krakow. Personally I would do Krakow for the Christmas markets. https://youtu.be/GCfaKx8xNhA?si=QXiIoZpyseBDgrBJ

There is also an Alicante (Spain) flight on Ryanair from Aberdeen on Tuesday. Thursday and Friday.

Edinburgh airport will have a wider range of destinations, and there is a direct, express bus to there from Aberdeen 24/7

From Edinburgh Jet2 fly to Funchal, Madeira on Monday and Thursday at 0925- on 27 November the fare is £68.85 each + £44 for a checked bag. Jet2 are a well respected discount holiday airline who also do flight only options.

Both Jet2 and Ryanair fly from EDI to Rome Ciampino. Ryanair also go to Bergamo and Bologna in Italy

Isn32c I avoided Edinburgh as I have been trying to curb my.... well, why?! You are correct!. It would be a disservice to fail to mention that from Edinburgh Ryan flies direct and cheaply to the most beautiful and cultured city with the most consistently highly rated Christmas markets, theater, music and holiday cheer in Europe. Budapest of course. (And the English in Budapest is very easy to understand, unlike .... )

Consider going somewhere warm, in Southern Europe or perhaps Egypt.

Yes, warm! This article lists the warmest. You will find a few, a very few, places where the high is at 70F. But do remember it is the high, not the average. Generally, these are places with vibrant warm weather cultures … do check and figure out what you will do in the off season. What do I know. There may be warm weather locations that are just packed full of winter activities. Doubt you will be going to the beach. Also check on how much rain. And know that while you may have a great time, you will be missing what the location is famous for and if you are like a lot of us, a return to see the destination at its best just aint going to happen. Here is a list to begin the research with: https://www.adventuresofalice.com/warmest-places-in-europe-in-december/ Then for weather I like weatherspark.com because they show the average and the probable variation off the average.

Thank you all for the suggestions and recommendations! This gives me a lot to consider (even places that I hadn't!) and I appreciate the flight info, as well.

maybe I should still hold off on that and go in the future when it
won't be so cold and dark?

You brought up another point, "dark." Dark is more of an issue in rural areas or areas where the entertainment and interest have anything to do with nature. In cities, some cities at least, and particularly in the holiday season the dark can actually work for the atmosphere and mood.

The length of the day isn't a function of East and West. it's a function of North and South, so you might want to look up sunrise and sunset times too. Weatherspark.com has that as well. Or go to a big city full of holiday lights and let the dark work for you.

In case you haven't read between the lines, my vote in the winter is one of 3 places 1) a city with culture and nightlife because winter is the high season for such things. 2) a ski resort and 3) any place the Hucho are running.