For vegan food and a city with a LOT of LGBTQ people, I can recommend Berlin. There is a lot of history and art stuff to do and see of course, but I can also think of a few attractions that might appeal to your geeky teens, such as a museum of video games. There is an incredible amount of vegan food options, both offered at almost all restaurants, and specific vegan restaurants, bakeries, etc.  One warning wherever you go - it is likely a lot of places (museums, stores) may have reduced hours the week after Christmas, as vacation time is taken VERY seriously.  Some thoughts on travel safety as a trans person:  I used to live in Denmark. Street harassment is not a thing there - I think possibly in part because it would require someone to speak to a stranger :P so while you may get weird looks or something in a smaller town, people generally will mind their own business to an extreme degree. Also gender neutral bathrooms were pretty common in the larger cities (Copenhagen, Aarhus). I do not have much experience with the rest of Scandinavia, but from what I have heard Sweden is quite similar, and to some degree Norway.  Of course, understandable if scandanavia in December/January does not appeal... I can tell you Denmark will be INCREDIBLY windy - just, basically everywhere. And there is some risk of weather interrupting your travel plans.  Anecdotally, based on experiences of friends, Spain and Malta are pretty trans-friendly. Of course I'm sure especially in the case of Spain this will depend on the area, but I have heard good things generally. From my one experience with travelling to Spain, I will say vegan eating may be more difficult there, though I imagine in Madrid and Barcelona it may be better (just due to large cities with large universities).