I know Rick's advice to stay outside of Naples (eg in Sorrento). Having visited Naples for the first time this past weekend, I understand that advice. However, I had a wonderful experience at the "Casa del Monacone", and wanted to suggest it for folks headed to Naples.
I could rave about it: perfect location, inexpensive, comfortable lodging, air conditioning, wifi, etc . . . maybe the simplest thing to say would be this: it made staying in the heart of an extremely chaotic, noisy, and dirty city into a pleasure. I haven't had a finer B & B experience anywhere.
You can find them here:
http://www.catacombedinapoli.it/casaDelMonacone.asp