We'll be staying near Pontremoli and driving around the area but have heard the villages are best seen via rail. If we drive down to the coast, where should we park and how much would it cost for the day?
As you’ve heard, the villages of the Cinque Terre are indeed better visited by train rather than by car. There is very limited parking at each and the roads are narrow and steep. So my recommendation would be to head to La Spezia and leave your car in the parking lot near the rail station (you should find free spots but check in case you end up on a paid area) and from here take the train to either Monterosso (most northern town) or Riomaggiore (the first town you reach). Connections to the Cinque Terre are short and run throughout the day. You can check theTrain Schedules ahead of time to better plan your day.
Since you will have a car, you can also make your way down to the coast to Massa and down to Viareggio, where you can enjoy both the sea and beaches as well as shopping, nightlife, pubs and discos, especially in Viareggio, Pietrasanta and Forte dei Marmi which become during the summer a really fashionable destination for Italian families and young people.
If you are seeking beautiful sea and you like rocks I definitely advice you to head to Livorno, which in addition to be a characteristic harbor town offers also beautiful landscapes and high rocks from which you can improvise sky diving, if you can !
Here you can park along the street, and walk down to the coast through natural paths which try out your deftness but show you gorgeous sights overlooking the blue water of the Tyrrhenian sea.
Especially advised is the sea at Calafuria, Livorno.
Agree with Sara and say that the best place to park and catch the train is in La Spezia and parking should not be a problem, either in the parking lot or on the street.
If the day is very nice, I also recommend trying the ferry - catch it at La Spezia to both Portovenere and to the Cinque Terre - you can see the schedules here and then take the train back to La Spezia at the end of your day. You'll experience a beautiful view of the towns and Portovenere is also really pretty.
We love Pontremoli as well, make sure to visit the museum at the castle there.... also visit the smaller museum at the castle in Aulla, both take you back in time!
Instead of driving to La Spezia, pick up the Parma-Genoa train in Pontremoli. They stop in La Spezia, where you can pick up a train to the Cinque Terre. Some of them also stop in Riomaggiore, which means you can avoid the crowds in La Spezia.