I would not spend 2 nights in the Cinque Terre these days, let alone two weeks. The villages were way too crowded to be enjoyable for us 12 years ago, and have only gotten worse. And I doubt they can be called fishing villages these days; tourism is the dominant industry there.
Depending on the month of your visit, I would recommend one of the villages on the Apulian coast. They are linked by train. We spent time there last March and would love to go back to spend more time. Our favorite village was Monopoli, with its charming oldtown of white-washed houses. I don’t know how active the fishing industry is there, but we did see the fishing boats in the harbor, observed men carrying buckets of calamari, small octopi, and sea urchins around. One fisherman came by the restaurant where we were having lunch to drop off his recent catch in a bucket. You can do daytrips by train to the larger cities such as Lecce, known as the “Florence of the South”, and Bari, a major port city’s but also a fishing town.
I have a nice book on Puglia, and will check to see what they recommend as the most viable fishing village.
Further north, in Molise, I been attracted to the town of Termoli, but we haven’t made it there yet. It is becoming known as a resort town, but still retains its fishing village character,
http://www.madeinsouthitalytoday.com/termoli.php
It was the photos on this small hotel’s website that got my attention:
http://www.locanda-sangiorgio.it/en/
To avoid most of the summer beach crowd at any coast side town, plan your visit between September and May. If you start in London in mid-to-late September (our favorite time to be in London, thanks to the month-long Thamesfest), the timing should be good for both the Swiss Alps and the Italy coast.
https://thamesfestivaltrust.org/
It is too bad that Chioggia, near Venice, has become a cruise port, or I might have recommended that.