In reply to cameron.ree:
The classic location is Città dei Sassi Passo Sella (chuck those words into Googly).
Bouldering in the modern sense (rather than just teaching beginners and having a bit of fun) is only recently getting popular in this part of Italy. Of course limestone rarely forms boulders while Dolomite does. Dolomite is good but not really the best for bouldering, not least because it gets polished quickly.
There is a huge potential in the Lagorai range on porphry rock and fantastic settings, largely unexplored. Val Daone with its white granite is becoming established as a bouldering hot spot. But both these area are a bit west of where you want.
Further north of Cortina you come to Alto Adige, the German speaking province of Italy and up there I believe there is a lot of good bouldering on gneiss and other types of igneous rock. Never been myself - not much of a boulderer, but I have a guidebook that says that (in Italian).
The season might be an issue. Passo Sella is extremely snowy at the moment and likely to stay that way for a good while. Presumably you are thinking high summer?