Salerno Day Trips

You can take the train to Paestum
No tour needed

You can take ferry to Amalfi then go up to Ravello
No tour needed

Yes, you can do quite a bit on your own using public transportation.

Besides Paestum...

Train to Naples, taxi to pizza or to the Archeological Museum
Train to Naples, walk downstairs and take the Circumvesuviana to Pompeii or Ercolano
Ferry (if running) to Amalfi or Capri
SITA bus to Vietri Sul Mare & any of the waterfront villages on the Amalfi Coast

We've based in Salerno twice and usually would take a daytrip, returning to Salerno for a nap, then a wonderful dinner at any number of great & reasonable restaurants in Salerno's Old Town.

While a very long walk or a taxi is involved, it is possible to take the local Trenitalia line from Salerno to modern Pompeii for the ancient site. Looking at, say, Google Maps, this uses the Amfiteatro Entrance to the ancient site, rather than the Porta Marina Entrance that is right at the Circumvesuviana (commuter line) train's Pompeii Scavi/Villa Mistiri station.

Edit: Trenitalia may have more than one stop with Pompeii in its name.

It's about a mile walk, Tim, all flat. We did it kinda by mistake, but as things happen sometime it was a good mistake. Beautiful late winter day, walked through Pompei-town, past a bronzed girder from the Twin Towers in front of their city hall, and then as you say you could walk to the Anfiteatro entrance, although we entered at nearby Porta Marina.

After 4 hours, however, the 'dogs' were tired so we took a taxi from the Pompei Scavi exit to the Pompei Trenitalia station and back to Salerno.