I second Ravello! Positano is also very nice. If you can, try to take a ferry into Capri from Sorrento. You can do a daytrip and it's fantastic. Procida is also great and less crowded than Capri.
I wish I was still living in Naples, I'd take you some a really good, really authentic Neapolitan restaurant that I LOVE. Too bad it's in the boonies and you do need a car!
Gosh, I miss Italy :\\\'(
June