I realize that her budget might not permit it, but most Europeans think nothing of taking a bargain-airline to someplace interesting for a weekend. I hope she can at least use the train to visit Barcelona or Madrid while she is studying. Paris certainly deserves more days than that. My own guess is that, because she has had the wisdom to broaden her school experience by studying abroad, that she will be in Europe again sometime, or multiple times. So it may not be necessary to make an encyclopedic trip at age 21.
Because the distances you describe are so large, and the visit times so limited, your route may depend more on the discount plane tickets you are able to obtain in time for May travel anyway. But if your question meant "along the way" (e.g. that you'll use some trains), I would consider Cologne, Antwerp, Brussels, as well as places in France like Avignon and around there. It appears to me that you are looking at major cities for a first-time visit to Europe. I can't recommend a list of 2-hour visits "along the way" for such a trip.
As another noted, Paris and Amsterdam are superb locations for easy and important day-trips. If any of her studies are cultural (I mean like Art History or World History) we might give different answers. Because you might be in the Netherlands during bulb-flower time, many people would consider Keukenhof a must - but only until May 18, 2014. I agree that Berlin is a very rich destination. You will only get a taste of Amsterdam in two days.
