If I were you, I would skip one (or two) of those day trips to spend 1/2 day in Pompeii and the rest of the time in Naples. Virtually all the art work, statues, mosaics, etc. from Pompeii are housed in the archeological museum in Naples. So going to Pompeii first and then to the archeological museum is a good way to get a good sense of what Pompeii was.

There is much to see in Naples while Sorrento is thick with tourists and tourist hawkers. The same goes for Capri, which is no doubt one or more of your day trips. Hopefully another of your day trips will be to Ravello and Amalfi. I often wonder why Naples is skipped for a stay in Capri, Sorrento etc.

Peter