Hi, we passed through Amalfi earlier this year (unfortunately early season so many things closed) but had a great time (as we have done there on other occasions). There's some info on our blog about a couple of fantastic towns further south and in the Puglia (top of the 'heel') area.
Didn't go this time round but one place you absolutely should not miss is the Roman city of Paestum, about 40 minutes south of Amalfi. Superb temple ruins (3), amphitheatres, ruined town etc that was only discovered about 100 years ago when road builders were putting a road through what was then swampland.
Best ruins outside Rome and, better still, few people know about it. Plenty of accommodation available around the ruins - beaches nearby.