There is nothing wrong with driving from Florence to Monterosso, as a matter of fact of all the many times I’ve been to the Cinque Terre from Florence, I think I’ve gone by train no more than a couple of times. In all other cases, I drove, for convenience and also for time. Unless you start from Florence city center near the SMN station (and my house in Florence was not in or near the city center), driving is a bit faster than the train. Considering there are 4 of you, it may not even be more expensive if you already have a car and don’t have to rent it solely for that purpose. The car also gives you the flexibility to go at your own pace, to leave when you want without being subject to train schedules, and you can easily stop along the way along the way, if you so wish.
The fastest way is to drive the A11 Firenze Mare freeway. After the Lucca exit you’d take the beltway connecting you to the A12 (follow directions to Viareggio and Genova after Lucca). Not far after La Spezia on the A12, the exit you’d want is the Levanto-Carradano exit. The total drive should be around 2,5 hours. There is no reason to exit the freeway system unless you want to. If you so desire, Lucca is probably the most logical choice, since the freeway passes by it. Pisa is not, because it would entail a longer detour, unless of course you must see Pisa at all costs. If either doesn’t work for you, because you’ve been there before, maybe Forte dei Marmi, will satisfy your needs, especially if you are in for some high end shopping at some famous boutique store or if you are interested in seing some fancy Villa of some Russian oligarch or some famous VIP on holiday (Andrea Bocelli lives there as well). If you are interested in seeing their yachts they are usually docked at nearby Marina di Carrara, not sure if Vladimir Putin’s is still there, after the Italian authorities tried to seize it after he invaded the Ukraine, but it’s usually there as well.
