"My" outdoor theatre at Il Piacere was inspired by this: the Forum, an open-air theatre-in-the-round at Ontario Place, on Toronto's waterfront. Under the canopy roof there were actual seats, but nearly everyone else is sitting on the hillside, on the lawn. In the winter of 1994/5 it was demolished to make way for the Molson Amphitheatre. I have wonderful memories of concerts I saw at the Forum. I'm sad that it's gone. That's most likely why I gave it a measure of immortality in this book.
The actual veranda at Il Vittoriale, named for Apollo (my fictional one was named for the goddess Diana). This would have been too cluttered a workspace for poor Alex, so I "redecorated" it a little in my novel.