Wife and I just got back from Naples/Capri/Amalfi/Sicily. It was hot, which we knew going in, but life schedules dictated that we go then.
Started in Naples, day trip to Vesuvius and Pompei but skipped Herculaneum.
Capri was awesome, but very crowded. Apparently, unbeknownst to me at the time, Aug 15 to 31 is a time of Italian holiday, so all the Italians take a vacation and lots of them go to...the beach. Which is better, I guess, than being overrun with American tourists or god forbid Chinese tourists. Highly recommend a private boat tour around the island. You can customize as you wish. Private boats have priority access to the Blue Grotto. We did around-the-island with stops at Blue Grotto and a couple of spots to jump in the water - crystal clear - 3 hours, for 180 euro, just me, the wife and Mario, the captain. Capri is one of those places you can stay either a day or a week. Lots of folks do day trips over from Naples or Amalfi. Ferry is cheap and fast.
We also stayed in Praiano on the Amalfi Coast. I think, if you're gonna stay on Capri, you should avoid Positano and Amalfi, as those towns are a lot like Capri.
Took a cab from Praiano to Salerno then drove down to Sicily, which is pretty much an easy drive if you want it to be. Freeway all the way, no tolls on that stretch of the Autostrade and ALL the drivers are extremely well behaved. Fast in the left lane, slow in the right. 30 minute ferry to Sicily from San Giovanni. Couple nights in Taormina, which is cool but somewhat touristy and a night in Palermo before driving all the way back to Catania where we flew out of.