Train to Sorrento, and then a boat ride fro Massa Lupense around and to Capri. We spent about two hours on the small boat (driver and 9 passengers) getting there, seeing various grottoes, the excellent rock formations known as I Faraglioni and the renowned Faro Punto Carena, a place apparently well known to J-J. Then we had 4 hours on the island before the return trip. Of the many thousands of tourists who descended on the island from a parade of ferries, I estimate that approximately two had come with the express purpose of hiking up to the ruins of Villa di Iovis, the Villa of the Emperor Tiberius. It could have been 4, but G&L had been there before and instead went to see the Villa of Nero's wife at Oplontis.
Capri is remarkably steep. We walked up to the main square, then started on the path to the Villa, only to be confronted with a sign saying it was closed for security reasons. That is, they don't seem to think it is worth the trouble to hire someone to admonish tourists not to break off souvenirs, so easier to just put up a fence. I doubt that anyone else on the island noticed. Then we regrouped and started on the path to the natural arch, a stunning feature, but currently undergoing repairs to forestall a fate like that of the old man of the mountains. We then reformed again, and set off on a path to a viewpoint over the arch. All these paths are paved walkways, but after a bit we saw a sort of hiking trail off to the side, disappearing up into some scrubby woods, and off we went.
After a bit we encountered a couple of older gents walking their dogs and chatted them up in a mixture of tongues. They thought it would be good for us to take a different trail that led to I Faraglioni, and then rejoined one of the paved paths and eventually led us back to the center from the other side. A very nice excursion. Some of our other shipmates had taken a chair lift up to the high point on the opposite side of the island, which would also have made a good excursion, but I think having been once is absolutely adequate, and I don't expect to return.