If you don't have a yacht, a friend in the mega rich circle, or the time to stay on the island of Capri a day trip is worth at least a short visit while in the South of Italy.
Since you aren't staying on the island you will have to catch the last hydrofoil back to Naples at 7 which means you have about seven hours after an early lunch. Keep in mind this also means you can't have dinner at one of Capri's world famous restaurants either. But what you can do is explore the island and its history in style.
As soon as you get off your boat it would be worth it to take a tour of the island on a classic-looking wood boat that holds about 15 people. This boat takes you as far around the island as it can (unless the sea is not cooperating).
Do head up to Anacapri by convertible taxi and grab a ticket to the Monte Solaro single chairlift that takes you to the highest point for the views of Naples, Mt. Vesuvius and the sea fading into sky. You can also take a hike to various spots around the island or have a much deserved drink at the top to calm your nerves from the heights.
Finally, head to one of two places...
1- Villa San Michele if you want a living villa with awe inspiring views and a place to relax.
2- Villa Jovis for a visit to the ruins of Tiberius' palace. Take a peak over the cliffs to see the drop many of his enemies took.
If neither of these interest you then head to Marina Piccola for some sun tanning, a drink and some seafood.