Don't miss Ravello, a tiny but lovely town up to an hill close Amalfi (15 minute by bus from Amalfi). Here you can visit 2 nice countryside old villas with a wonderful view on the coast.

Visit Ercolano (by Circunvesuviana, the local train), same history than Pompei but smallar, less crowded and better preserved than Pompei.

If you are interested in and you have time, in Minori (a town a few kms from Amalfi by bus) you can visit digs of an interesting Roman villa that is in the middle of the town (it is free).

In Amalfi take time to discover it white narrow pedestrian streets off the touristy main street: you'll find the real Amalfi with people that enjoy talk to you (if you can speak Italian). It recalled for me Greek island towns!

Enjoy Amalfi coast as I did! Marco in Milan - Italy