Where would an 18-yr-old social studies student appreciate most?

In the Czech R. it would be Prague.

What interests does she have in art, history, outdoors etc? I have kids a bit younger 14 and 16 and they are way more invested if they have a say and take their interests into account.

Two hours is a very limited amount of time. If you fly anywhere, you'll need close to three hours just to get to an airport and through the security hoops to the departure gate. I'd figure 5 to 6 hours, minimum, when a flight is involved. Places like the Italian lakes require first a flight, then a transfer to the train station, then a train ride--adding up to the better part of a day. So I'd nix Milano/Lake Como for logistical reasons. Ditto Greece. I wouldn't go there for just a few days; it takes time to move between Athens and the islands. On a short visit it would be a bit stressful, making sure you were back in Athens for your outbound flight.

I don't know how many days you have for your add-on destination. Is "a few" three days? five days? more? That would make a difference to me. How long is the total trip?

And how are you getting home? Will you need to return to Amsterdam or Brussels for your return flight, or do you have the flexibility to book the return flight from your add-on destination?

Not being a fan of long transportation legs that amount to skipping over interesting areas I'll just want to return to later, I'd be looking at western Germany from among the places you mentioned. Your other options are nothing like a 2-hour trip away. Western Germany has historic towns to go along with the beautiful scenery. For that matter, the Netherlands is much more than just Amsterdam.

Any reason why you didn't mention Paris? It's reachable by fast train from Brussels in less than 1-1/2 hours (though there may be an advance-check-in requirement for the Thalys). London is less than 3 hours away by Eurostar (which does have an early-check-in requirement). It's not that those are better options than Austria, northern Italy and Czechia; they're just more geographically convenient in this case.

2 hours on a train is two hours, centre to centre.
2 hours on a plane is more like seven - an hour to the airport, 2 hours wait and security theatre, 2 hours on the plane, an hour getting off the plane and out of the airport and an hour to the centre of wherever you have gone. That around 7.

Big diff.

Thanks so much for all the responses. And I just discovered the General Europe forum, so please excuse my duplication.

She has much interest in art (always in school choir and drama and loves museums, classical and modern), and history as it explains culture today. Problem getting her input is that she always so appreciative of "anything! wow Grandma!" so I'm digging to find out how to get her true interests. This is for her.

Got it about allowing extra hours for air travel, I'll allow a full day if we fly anywhere within the trip. No, we don't need to return to Amsterdam for the return flight.

The number of days for this secondary destination is very flexible. If we love it, it could be a week including all the logistics. Total should be 2 weeks including travel, so we also need to nail how much time we spend in Netherlands and Belgium.
She did rule out UK and Spain because she has other options to travel to those in the future, and no France interest just because. Her aunt and I said ok to that just because we have to eliminate. She's very interested in Germany, Austria, and Czech Republic because of her maternal ancestry being from them recently.

That additional info helps a lot. I'll bow out at this point since your target areas are ones with which I have limited, if any, recent experience.

Except I will note that Berlin (while not full of beautiful historic architecture unless you hop over to Potsdam) is blessed with magnificent museums. It also has a wealth of WW II and Cold War historical sights. If her interest is more in the older periods, Vienna might be equally good, and I believe it has more surviving pre-war architecture. Berlin also happens to be a very youthful, vibrant city; I think that would appeal to someone your granddaughter's age.

Thanks acraven. Berlin has come up in my research for recent huge change, really interesting for anthropology perspective and sounds like a city of the near future.

I spent six days in Berlin in 2015, and that was definitely not long enough. Quite a number of museums remained untouched, and I had very, very little time for just walking around, which is something I normally like to do. Another plus for Berlin is that it is one of the least expensive capital cities in western Europe.

I'd like to encourage you to try again to get her involved in the detail planning for both parts of the trip. Kids of her age get really owning a trip that they put together - ownership is a wonderful thing - especially if they know they will be supported when something doesn't go the way they planned it.

You may be surprised with what she comes up with....

acraven, good to note. We don't want to be frustrated by cramming. We are the type to "grok". Nigel, I'll be looking for ways to get her to get active in this. I have to convince her it really is for her.

Maybe play the "You youngsters are so much better at Internet research than my generation is" card?? But then at some point you need to get her to look at guide books, too.

"She is very interested in Germany and Austria...." Where in Germany? Which specific area? A very valid reason for her interest because of a specific family connection. . I spent eight weeks of my 12 week trip in Germany plus Vienna the first time over and I don't have any family ties to Germany.

As a middle school teacher - not high school, but feel I am in touch with that generation fairly well - I would second the suggestion of Berlin and environs. While Prague has wonderful architecture and is one of my personal favorites, Berlin has an historical mystique, a multi-cultural vibrancy, and a strong place in 21st century politics. It holds options for exploration in the forensic psychology of wartime Germany, Cold War sociology and, in particular, a visit to the highly regarded Pergamon Museum to satisfy the anthropologist.

"Berlin has an historical mystique...." How true, when you know the culture and history of the city, not merely the Nazi period, in the realm of Prussian-German history.