How To do Bouldering

My friend and I are studying abroad in Florence, Italy for this coming Fall semester. We have plans to go over 3 weeks before the semester begins and are currently looking at doing an extended (two week) hike through the Alps. We are flying into Rome. Are there any suggestions, of where to go or entrance points? We are just looking for a place with excellent sights and good hiking, and possibly bouldering? Thanks

North Italy: Dolomiten and Brenta
Switzerland: Engadin and Bergell

are the best areas from my own experience. Google the names or come back to me if you want to know more.