Disagree with Penelope on skipping Capri, but IMO a few hours in the town was plenty. We hired a boat in the town of Amalfi and did a 1/2 Capri tour (was like 5 hour round trip, with multiple stops for swimming).
Any reason why you are definitely not renting a car? My wife and I had one, and frankly I'm not sure how we would have gotten around without it. I know people do it, but it takes a lot of planning, and then tearing up those plans because it's Italy and nothing runs on time.
If you are outdoor people at all, I highly recommend the Path of the Gods hike. It was one of the most memorable days of my life. Started in Bomerano in the morning, hiked to Nocelle, then down to Il San Pietro de Positano hotel to eat lunch at the Michelin starred Zass for lunch. We packed a change of clothes in our backpacks. Had a 5 course tasting lunch (really more like 7-8 with the extras they bring) with wine over about 3 hours, then changed back into our hiking clothes and hiked back the way we came. Even stopped in an old abandoned shed along the way back close to sundown for a quickie. The hike was absolutely amazing.