Train or Driving from Venice to Cinque Terra?

Train times: www.trenitalia.com/tcom-en

Enter the Cinque Terre village where you are staying in the "TO" field and Venezia S. Lucia in the "FROM" one. Pick up an early hour of departure from the drop down menu.

Trenitalia 's site is programmed to show always the quickest itinerary, so if you want to change only once at Milano Centrale you must enter Monterosso as arrival station. Going via Milan will take more, but you'll have reserved seats all the way to the Cinque Terre.

Realistic driving times, tolls and gas costs: www.viamichelin.com
Are you going to stop somewhere along the road? If not, I can't see any reason to drive through the mountains when there is a train that can do it for you. More, you'll have either to find a place with parking or drop the car off at LaSpezia and then board a local train.

Watch out for camera controlled ZTL areas in cities and for speed traps on motorways.

Taking the train in Italy is a true pleasure and inexpensive. It also often (usually?) takes less time. Take the opportunity to travel like a local and skip the car. Darioalb has given you excellent advice.

Throwing my vote behind darioalb and Laurel: rail is (usually) the fastest, most stress-free method, and especially for this trip since you do not want or need a car in the Cinque Terre. If you were intending on staying in, say, an agriturismo in Tuscany for a couple of days, then a car is useful but they're usually more hinderance than help for city-to-city or many town-to-town trips. Stations are usually located right in the middle of the action where it can be more difficult (or even impossible, in the case of S. Lucia in Venice) for cars to go.

Italian trains are indeed an enjoyable mode of transport as they'll allow all of you to sit back and enjoy the ride without concerns about speed cameras, unfamiliar signage, parking, avoiding ZTLs and pedestrianized areas, or safety of belongings left in a car at stops along the way. So far, trains and the occasional bus are the ONLY types of transport we've used in Italy.

I enjoyed driving in Italy but there is nowhere to park in Cinque Terra and a vehicle would be a deep hassle. Streets are tiny and winding. We went by train and it was just fine.