From Montecatini, take a train to La Spezial. And then a regional train to one of the several villages known to be a part of Cinque Terre. This is a picturesque set of villages set along the Italian coast.
I was there on a Sunday so it was quiet empty. I highly recommend a gelato place that also serves Sicilian ice treats!
Vernazza, Cinque Terre
I only went to one town, Vernazza, and it was packed. There was a recommendation to go to one of the towns, but I went to the wrong one. Oh well, it was an interesting experience anyway!