Day trip to Capri
 

I found Capri easy to visit on my own, but I didn't go to the Villa Jovis.
FWIW, the Villa Michele is, IMO, absolutely stellar.

Agree with KJA. I would visit on my own, but then, I do not prefer traveling in groups unless where necessary (can't now think of an instance where it's necessary, though!).
I'd go on my own and go as early as possible in the morning for better light and possible avoidance of the bulk of the day trippers.
I've never visited Capri on a day trip, though.

Our first visit to Capri was for just a day from Sorrento. We saw quite a bit of the island using the island's bus service. We purposely didn't go to Villa Jovis or take the boat(s) into the Blue Grotto because we knew they would take up a lot of time. We did ride the chair lift from Anacapri to Monte Solaro and visited Villa Michele which remain the highlights of that day. FWIW, there are other villas, forts, a lighthouse, view points, etc., and there are multiple grottos (verde, bianco, rosso). On subsequent trips, we road the chair lift again and got around to seeing the other sights, some by chartered boat. If it's a good weather day, I don't think you'd go wrong with any plan.

Enjoyed both the walk to Villa Jovis and a visit to San Michele. We were pretty much on our own for the former after the first few hundred metres out of town, while getting to the latter involved a bus that had to crawl through traffic.
Can't recall how long each visit took. We stayed overnight.

I agree that on Capri you can do things on your own without any difficulty. If you like walking there are some lovely footpaths and you should be able to pick up a footpath map at the Tourist Office. Definitely ride the chair lift from Anacapri to Monte Solaro and visit the Villa Michele, weather permitting.