Day trip to Capri

I'll recommend exploring the island on your own as it's sometimes easier to move more nimbly when not in a group, and you can spend as much or as little time at different spots as you wish to. It's not a difficult place to do independently either; just be sure to get a map at one of the tourist shops as you'll need it for finding your way around on foot. The web of "streets" are more like narrow lanes not wide enough to accommodate vehicles (although there are a few streets of normal width.)

We did do the hike to Villa Jovis and can highly recommend it. The view up there is wonderful, and it wasn't as overrun with other tourists as the easier locations to reach. You do not need a tour: hours and directions for how to get there are here:

https://www.capri.com/en/e/villa-jovis-mount-tiberio

Here's someone's nice blog piece for some more pix and info:
https://www.travlinmad.com/blog/tiberius-capri-villa-jovis

Tip: after your visit, make a stop at the little cafe - Bar Jovis - that's along the way, not far from the ruin, to rest your heels and have a beverage/snack before making your way back.
https://www.tripadvisor.com/Restaurant_Review-g187783-d2298236-Reviews-Bar_Jovis-Capri_Island_of_Capri_Province_of_Naples_Campania.html

I'll also recommend this walk:
https://www.capri.com/en/e/pizzolungo-2

And if you have time to get up to Anacapri, (take the little bus; you can hike the mountain but you probably don't have time) do the chairlift up to the top of Mt Solaro. There's a cafe up there too. My DH is nor wild about heights and did just fine on the chairlift: you don't get super high off the ground.
https://www.capri.com/en/e/monte-solaro-high-drama

We enjoyed walking around the village of Anacapri more than Capri; it felt a bit less glitzy/posh.
Be sure to have a granita al limone from one of the stands around the island: so, so good when you're hot...and even when you're not. :O)

Also be sure not to miss the last boat back to Sorrento: they do not operate after dark, and that last boat will be crowded with others making the most of their time on the island.

Have fun!! :O)

Thank you Kathy. You have great recommendations.

To that good reply, I'll add:

More than one ferry company does that route. But Company A will not tell you, "You could leave 35 minutes sooner if you go over to the Company B ticket window!" Both companies will urge you to buy your return ticket (specific departure time) before you go over. Even in early May, I think that is a good idea. This area has heavy, year-round demand for tourist services. (We were there in the last week of May, and everything was JAMMED.) Do not expect ANY outdoor seating on ferries to Capri. I guess the water can be sometimes too rough. Our outbound ferry had about 200 airline-style seats in a sealed cabin. Our return ferry was more like a tiny Staten Island Ferry, with cars and trucks below, and hundreds of STANDEES everywhere. Could not move around any better than on the CIrcumvesuviana! I did manage to buy a beer.

Note that the ferry you go home on may be much bigger than the one you went over on. I mention that because it could use a different slip, 1/4 mile from the one where you arrived from Sorrento. I suppose there must be a chalk or LED board that tells you this, but we didn't see it in time.

We chose to take the Phoenecian Steps towards the ferry on our return. That is still sunny and hot, but it does lead directly to the ferry port, with a view of the big local beach on the way. I am not sorry we went to Villa Jovis, but if you've been to Pompeii, Herculaneum, and Oplontis or Hadrian's Villa, Villa Jovis is much more "ruined" and archaeological. It did seem like a 2 mile walk, uphill both ways! Good views, interesting place despite desolation. That cafe was either closed or had little to sell, our day. I forget.

We had to try more than one casual restaurant to get a seat for lunch. Many places were booked up. You will want to sit down and rest, out of the sun, for your lunch. You can expect to walk four or five miles if you make the most of a day on Capri. (Not saying you MUST, just emphasizing the vast size and the mostly pedestrianized (no bus, no taxi) areas. City bus was laughably small (smaller than a car rental bus), could not get on it for the crowding.

All this is not a slam, we had a great time. Just some more information. We were sorry to see the same international unaffordable boutiques now on Capri, as well as downtown Rome and Paris. (And Positano.) We used Lonely Planet Italy to find out what we should trek to. We aren't "tour guide" people, but I can't imagine seeing as much with ANY group tour. Maybe a private tour, with a young, spry guide??

The RS book has a nice section on visiting Capri. We got down to the Sorrento docks by 8am and at 8:10am were on a ferry. Early really is better, there were no lines for the bus tickets and the bus on Capri. We made the mistake of following the RS itinerary and taking the round-the-island boat trip right away. By the time it finished the line for the mini-bus up Anacapri was long at was going to take at least an hour. We ended up splitting the cost (30E in 2023) of a taxi up with another couple to avoid wasting the time. If I was doing it again I'd go up to Anacapri as soon as we arrived at Capri and do the boat tour later in the afternoon. Or if you want to do the Villa Jarvis hike then go up to Capri town right away, don't do the boat trip first.

When you arrive take a picture of the departure times of the boats on the display board which shows all the lines. Then in the afternoon you can decide which one you want.

As with an earlier poster, we enjoyed the chairlift up to the top of Mt Solaro. There was a line of perhaps 100 people but they're putting someone in the lift every 5-10 seconds so it went quickly.