The hike up to Villa Jovis will give you exactly this.
Again, you will be among many more backpacks and selfie sticks as you stroll around the Piazzetta. But now the beautiful views are beginning to come into view and you start to realize that indeed, it was a good idea to come here.
Getting there gives you an opportunity to walk through a winding maze of narrow streets with views into the charming courtyards and gardens of its residents.
From the Piazzetta, walk the length of Via Longano, continuing along Via Sopramonte and finally Via Tiberio. It's an uphill walk about 1.25 miles and with take about 46-60 minutes.