My DW and I spend a couple of weeks touring the Amalfi coast a couple of years ago in mid-June. It was already crowded (presumably less so than in mid-summer), but still wonderful.
We spent most of our time hiking (interesting, steep trails), sight-seeing and eating!. We started in Geneva (where we'd been on business) and took the train down to Florence for a week (also wonderful). From Florence we took the (super-express) train to Salerno via Naples. We caught the bus to Amalfi (there's also a ferry) right in front of the Salerno train station. Spent 3 days in Amalfi, then bussed to Positano for two days (also took the express ferry back to Amalfi after a hike), then to Sorrento for 3 days, then the ferry to Capri for 3 days. Then caught the morning ferry and spent a day museuming, sightseeing and eating in Naples, before catching the express train for a short week in Rome before heading back to the U.S.
In Amalfi, Positano and Capri we did a lot of hiking. From Sorrento we took the commuter train to Pompeii, then a bus to Vesuvius, then a bus to Herculanum, then the train back to Sorrento (long day!). We really loved Amalfi and Capri (which surprised us...good hiking, great restaurants, and quiet once the ferries left in the evening!). We thought Positano was beautiful (but a bit too crowded and touristy). And found Sorrento surprising charming and a great base for sightseeing. Naples was a bit gritty, but a great archeology museum and incredible pizza! The towns and trails in the hills (Ravello, the pathway of the gods, etc.) were truly remarkable! (There are a couple of (somewhat dated) hiking guides that are essential, since the trails are unevenly marked.).
Yes, the buses can be nauseating but they are convenient and cheap and essential for getting to some of the trails. While expensive, the express ferries are quicker and far more comfortable. There were a couple of pre-packaged independent hiking trips we considered (on foot travel, etc.), but they couldn't get the hotels we wanted, so we booked everything ourselves on line, which wasn't too difficult, even in June! And the trip substantially exceeded our already high expectations!