I'm interested in hotel recommendations for staying in either of these cities. Also I would appreciate the views of experienced travelers on whether a group of American university students would get more from spending the entire 2 weeks lodging in Amsterdam and traveling to other Dutch cities or lodging in Utrecht or Leiden for part of the time.
I cannot comment on Utrecht but we made a bus connection in Leiden to go to Keukenhoff Gardens. Leiden seemed to be fairly small--smaller than Haarlem which is sometimes an alternative to staying in Amsterdam. I would imagine students would prefer Amsterdam.
Leiden's a great town to make friends, since it's a university town too....but not a lot there...it is small. Utrecht, to me, is one of the undiscovered gems of the Netherlands, with its wonderful sunken canals, shops, and restaurants down at canalside. It's twice weekly market just outside the main train station is massive! BUT both of these can be done as day trips from Amsterdam and area. Distances are so small in the Netherlands, and public transportation so inexpensive, it would probably be best to base yourselves out of Amsterdam-Haarlem. That way, you could range south AND north of Amsterdam....the north is also wonderful, and not as busy as the south. If you're going in the summer, the beaches at Katwijk are the best in the country!