My 2 cents... Lake Garda, beautiful, plenty of high end accommodations and lots of kid stuff.

http://www.lakegarda.com/parks-and-entertainment.php

Have fun whatever you choose.

As I said in my first post: "high-end accommodations that have apartments for a total of 20 people are in the countryside; they are not in lively places with lots of restaurants, cafes and interesting shops" and "high-end resorts are ... few and far between in Italy". San Clemente Palace is at least close to "restaurants, cafes and interesting shops".

But if that doesn't tickle your fancy and if your definition of "beautiful" is scenic rather than architectural, Google Capri and Positano (higher-end than Amalfi), click on Images and decide which you think is more beautiful. It will take three hours to get to either from Rome, even longer if driving. Choppy waters are rare in June, and you haven't said that any of the kids are subject to motion sickness. Since apartments are out of question for four days (weren't they always: in your other thread you seemed to want daily housekeeping), it will have to be hotels. For lively on Capri, choose a hotel that's near the Piazzetta; in Positano, one that is *in* the village. Be prepared to pay more on Capri or in Positano than at the San Clemente Palace for accommodation of a similar standard.

If you're prepared to consider less than absolute top-end in hotels, restaurants, cafes and shops, consider Sperlonga: closer to Rome (about two hours driving), beach for the kids. Google Images of Sperlonga to see if you find it sufficiently beautiful.

Zeppole, thanks - I understand what you're saying and yes, may be considering Venice and Amalfi Coast.
Zerlina - San Clemente is looking great and Positano may be a good choice too.

I think in our case the key maybe where we'll get accommodation since we need so many rooms and we can then take a call...

Thank you all!!!