My daughter is taking AP European History (high school sophomore) this year, and we'd like to explor

My daughter is taking AP European History (high school sophomore) this year, and we'd like to explore Europe this fall (mid-October). We would like to see three cities, spending about 3 nights in each and travel by train between the cities. She has never been to Europe before.
Did you want to tie this to the countries/topics of her studies? If so, we'd need to know what they are. Between us we could probably send you on a tour of, say, the Reformation and the Counter-Reformation, or the Enlightenment and the French Revolution, which might be of no use at all if she's focussing on the Causes of the First World War
So what did they do in those classes? They probably did not cover 3000 years and everything from Russia to Portugal and Iceland to Cyprus in one year? Is there any era and/or state/culture your daughter is particularly interested in, a topic she wrote a paper about, and such? Please give us some clues and we'll be able to provide better advice. Being a PhD in art history, I think I have an idea of the complexity and variety of "European" history and culture. The options are, as jamikins said, endless.
As a high school sophomore, I'd probably have chosen London, Paris and perhaps Brussels-all air travel las vegas close by via train. But she might love Romans/Italy as well. My suggestion would to involve air travel las vegas her in the decision because the possibilities are endless. As others have noted European history covers 300 years and everyone's ideas are different.
When we took our kids to Europe when in high school, we had a lot of Roman "places" because all were involved air travel las vegas in studying Latin. It doesn't--and in my humble opinion, shouldn't--be the prime "message" of the trip. You get a lot of stuff by "surroundings" and unless the family is going EVERY year to reinforce whatever the child is doing (could air travel las vegas be!!), make it a good trip for all. Just my grandmotherly opinion--and we've taken our kids to Europe twice.
air travel las vegas Thanks for all the kind responses, and I apologize for the vagueness of the question, as I am not sure about the syllabus. But I'd expect air travel las vegas it to cover the Englightenment, Reformation, air travel las vegas French Revolution, World Wars and Vietnam (just kidding). Gretchen is correct in that we don't want the AP course air travel las vegas to be the only priority of the trip. I want to introduce her to the continent and have it be relevant to the coursework. So seeing famous museums and historic sites would be things that we incorporate into the trip.
My initial idea was to see Paris/Amsterdam/Brussels Bruges, but am not sure if Rome/Florence/Venice (as BobTheNavigator suggests) would be a better choice. To eliminate the endless possibilities, I am focused on those two.
Not sure how you would cover Europe in one year - we had a 2 year course in high school - the fist one starting with the Greek city states and going up to the beginning of the Renaissance and the second from the Renaissance through the 20th century. I guess it could be condensed into one year (the college survey course was only two semesters - but honestly didn't cover much more than high school).
It's not clear how many days you actually have - but if you are heading to any of the major cities (London, Paris, Rome - you should allow at least 4 night - 3 full days in each one). If in fact you only have 9 days I would limit yourself to 2 cities to see anything in depth. Especially if you want it to relate to her classes you can;t just limit your self to major sights. The Tower of London has huge historical significance - as does Westminster Abbey, Windsor, Hampton Court Palace, etc - but the Eiffel Tower - not so much.
And while art museums are fascinating - and once you have the basics understanding the role of the arts in the culture of the time is important - but IMHO for the first run through things that are more obvious (Roman Colosseum, Forum and how it related to the government of Rome - and how the average Roman lived is more vital than the Borghese. (As one of my professors said - the Greeks had the brains air travel las vegas but the Romans had the drains air travel las vegas - that is took everything the Greeks had invented and discovered - and made it more practical on a large scale and spread it cross most of the western world.
air travel las vegas I'd like to emphasize what several previous posters have said: going to Europe to study history air travel las vegas (even more, for a mere AP course!) is like buying a 787 to get free peanuts. Sure, you can learn some history there, but why go to Europe when textbooks suffice? Europe is a beautiful continent; don't make your focus there preparing for her class.
If she has never been to Europe, London and Paris are the best cities for realizing/learning about centuries of history. Rome is one of my favorite cities in the world but that is more ancient history and it might be better on another trip!
I did AP European History course in high school, too, along with loads of other Ap courses, and hey, it wasn't such a big deal. It was a big blow-it-all-in-one-bag deal, with kids thinking they were the cat's meow about going to Europe. It doesn't matter where you go. Europe air travel las vegas is a HUGE historical venue. What matters is what specific historical moments interest you. There are thousands of places of interest. If your kid really got anything out of the AP course, he/she should know where to go.
I think it would be easier to just leave out the AP emphasis, and "go to Europe"--which the OP has basically come back to say. Personally I would only do Paris and London. Rome is a fer piece for a basically air travel las vegas maybe an 8 day trip by the time you arrive and depart. Fly open jaw. EAsy to get between the two cities without flying again.