Ciao Lianne,
I'm glad you found us and are finding the site useful!
I think the order you have your itinerary is actually the best: I assume you're renting the car out of Florence once you've decided to head out of the city, that's correct? I agree with that since you don't need a car in Florence at all, nor in Rome.
I would likely do Lucca as a stop as you drive from Siena to CT instead of from Florence, and instead just concentrate on those 2 nights in Florence.
As far as CT, since you'll have the car, I suggest staying in either Monterosso or better yet, Porto Venere, south of the 5 towns. Porto Venere is very charming and can be reached by car only so it is often a bit less visited that the other towns, and from there you can take a ferry to Riomaggiore and from there also catch train to the other towns of the Cinque Terre.
Another option is Levanto, to the north of the 5 towns. This one is actually connected by train so it also gives you that option for moving around. Once you're ready to leave CT, you can drive to Lake Como, that way you keep the car since you'll need it for that area.
You won't use the car at all in CT, so definitely look for a place that has parking included.
Let me know if you have any other questions we can help with!

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