We spent 7 nights there in Dec 2011 and found it was about the right amount of time. The Day # below is just for enumerating. Personally I'd do "Day Four" first.
Day One - Pompeii with possible stop also at Ercolano although to me that's too many ruins in one day. Be the time you get a train, tour Pompeii, get a train back, it will be at least 5 hours, and that doesn't include lunch. Go early to beat the heat; arrive at 09:00 if possible.
Day Two - Amalfi Coast bus trip. Do not drive as you will want to enjoy the views! Stop if you like in Positano, too. There's a nice walk from AmalfiTown to Atrani outlined in Rick's guidebook. this is a full day.
Day Three - Capri
Day Four - Naples day tour. See the Archaeological Museum before you go to Pompeii and follow Rick Steves' self-guided day tour. Another long day - you will be tired but it's am interesting day!
You could spend another day just relaxing in Sorrento, doing laundry (there's a decent laundromat!) and enjoying what Sorrento has to offer as it's very cute with great views over teh bay.