On our Italy ABD, part of our group did a side-trip to Pisa during our free day in Tuscany (not worth it IMO for a quick photo-op, but understand that it's on kid's bucket list. We swam and did laundry!)
Highly recommend Pompeii/Amalfi Coast!
What we did:
-flew into Rome, dropped most bags @ ABD hotel for storage and took bullet train to Naples, local train to Sorrento. The train is a blast! 200+mph! Swam and battled jetlag.
-next morning, hired a local driver to take our family down the Amalfi Coast. It wound up being our favorite day of our trip!
-next morning took train back to Rome with a morning stop at Pompeii (they have a safe luggage storage at the station)
Hilton Sorrento Palace has family rooms, great included breakfast with views of the Med. Sea and Vesuvius, and a pool that beats many Magic Kingdom hotels.
I'd do it the same way again (unless flight into Naples is doable).