i would like to use public transportation as noted below. Is it practical?

Villefranch to Nice or Monaco
Livorno to Pisa
Citivechia to Rome or north
Tarquinia

I know that it's practical for Livorno-Pisa and Citiv...-Rome. See the notes at portreviews.com. We were there last year, but did the cruise ship "Rome on your own" excursion. They provided the bus and meeting times, but we were free once we got to Rome. That way if there was problems with traffic, they would wait for us. If you're on your own, they won't wait.