capri

Renting a car isn't a possibility: visitors aren't allowed to bring or drive them on the island during the warmer months.
https://www.capri.net/en/e/getting-here#:~:text=For%20most%20of%20the%20year,there%20is%20excellent%20public%20transport.

The hotel's website states that they are accessible to the town of Capri and the port by bus. You will be walking distance from the center of Anacapri...which we personally enjoyed more than Capri town.

https://www.villaceselle.com/en/location

Reviews on booking.com should be helpful regarding location:
https://www.booking.com/hotel/it/villa-ceselle.html#tab-reviews

You might want to have your luggage portered to the hotel when you arrive at the pier. There will be a cost but that may be your opportunity to explore Capri town before heading up to Anacapri, especially if you arrive too early for check-in. Scroll down to "Once You've Arrived on Capri" on this page:

https://www.capri.net/en/e/getting-here

As explained on this "Getting aorund" page, there is also (expensive) taxi service on the island. It doesn't look like one could deliver you right to the door of your hotel but would likely drop you off at the intersection of Via Monticello and Via Ceselle.

https://www.capri.com/en/e/getting-around

You can use the bus or taxi to move between Anacapri and Capri. I stayed in Anacapri for 3 nights in April and if I had to do it over, I would stay in Capri because Anacapri gets pretty empty in the late afternoon and evenings after the day trippers leave. There's also more to do in Capri. Anacapri has Monte Solaro and Villa San Michele but Capri has Giardini di Augusto and several walking paths and is livelier at night.

Wouldn't it make any sense to spend two nights in each?

Wouldn't it make any sense to spend two nights in each?

No. I would stay in Capri, and I think 3 nights is enough. With 3 nights you can see everything without rushing.

If you like to hike, Capri (Capri town side) has several nice walking paths with great views... (just type these names in google maps for directions):
- Natural Arch
- Belvedere Tragara
- Faraglione di Terra
- Capri Overlook
- Belvedere di Punta Cannone

Thank you. We do like to hike. Just hoping it's not too hot. Couldn't make up our mind between this region and Milan, lake Como and the Dolomites but have decided to do southern Italy. First 2 weeks of October.

The Capri website also provides directions for many of the hikes:
https://www.capri.com/en/l/hiking-and-walking-trails-capri

No need for a guided tour; just get a map at the visitor center (HIGHLY recommended; the island is a rabbit warren of meandering routes) and follow the directions.

We really enjoyed the hike up and over Monte Solare from Capri to Anacapri. Also the Fort Trail (Sentiero Dei Fortini) along the cliffs on the west coast of the island.

Thanks Everyone for the input. The more I Iook at Amalfi, Positano, Sorrento, though I'm sure beautiful, and a place I've always thought I wanted to go to, the area must be the touristy of tourist traps, thus my idea of spending at least a few nights in Ana Capri. We've bought airfare to Naples and so we're kind of committed for the first two weeks of October, though I am hoping it won't be too hot and crowded. The crowds we can deal with, but I am concerned about the heat. Any thoughts?

We've been to Capri in early October and didn't find it too warm to hike/take long walks. Then again, every year is different so YMMV.

YMMV? Thanks for the encouraging words.

YMMV = your milage may vary, meaning situations can differ.