The only parts of Italy I've been are Milan and Verona and the trains. I'm guessing the trains are faster than they were since the 20-some years since I've been. Italy wasn't a good nation for day trips from other places then - from what I remember, it was a pretty long train ride between Innsbruck and Verona and Nice and Milan or Milan to Geneva.
I agree - lovely place but was very crowded the day I was there this summer. Enjoyed the boat trip along the Amalfi coast though plus neighbouring towns like Positano Capri.