Trying to come up with an interesting place to go for three days after a week on the Amalfi Coast this summer. Appreciate any ideas.

What do you like? What haven't you seen in Italy between the Amalfi Coast and Rome? Pompeii? Herculaneum? Oplontis? Naples? Sorrento? Rome? Another 3 days on the Amalfi Coast?

What kind of atmosphere do you want? If you want hectic and crazy - Naples or Rome. I'm assuming a week on the AC would be relaxing and if you want to stay in that mode - maybe Sorrento with a little jaunt to Pompeii.

The Sorrentine peninsula would probably be my choice.

OR: Sperlonga? Gaeta?

Are you driving?

I have 3 suggestions for you:
If you still want the sea, the coastline around sperlonga, anzio, and nettuno, all the way to ostia, is buzzing in the summer.The American War Cemetery is in Nettuno.
As for the interior, off the A1 is the spa at Fiuggi, which has drawn tourists for centuries , particularly since the water is thought to have medicinal properties. Fiuggi is an elegant town with many fine hotels and places to eat. Ingrid Bergman and Roberto Rossellini chose, after the filming of Stomboli, to have their child born in Fiuggi.
The Castelli Romani("Roman Castles"),betwen Fiuggi and the airport, have been summer retreats since the time of the Ancient Greeks and Romans. The pope's summer retreat is in one of the towns. The area has a reputation among Romans for fine food; a decade or so ago, the New York Times reviewed a trattoria there that the NYT proclaimed made the best saltimbocca in Italy.
You may find some videos in the Lazio Channel of www.WebVisionItaly.com helpful in making your decision. No matter your choice, do be sure to make reservations . All these areas are particularly crowded June and July weekends and during all of August

How about Orvieto, an hour's train ride north of Rome?