Not contradicting what Donna has suggested, as Lucca's train station does not have a baggage deposit area but there IS a company that offers it right outside the station. So you CAN visit Lucca on your way to Florence. The luggage deposit is in the square in front of the station, to your left as you exit. Here's the link to the store that offers the service:
http://www.touristcenterlucca.com/se...li.php?quale=2
So you can take the train down from La Spezia, stop in Lucca, drop off luggage and enjoy several hours there (maybe all late morning, enjoy lunch and head on to Florence in the late afternoon/early evening). The same shop offers bike rentals, so I suggest renting bikes to go around the entire wall that surrounds the historical center of Lucca
Then as Donna suggested, you can head on to Florence -- if you've never been, I recommend staying a day or two in Florence, and then only after that picking up the car rental when you're ready to leave. I'd suggest the
Chianti area as a great central location to stay in - you can drive around Chianti, go to Siena, San Gimignano, the Val d'Orcia. Of course, 3-4 days will barely be enough, but you should be able to fit in quite a bit, just remain flexible with plans.
Also recommend to not rent the car from the Florence airport - there are agencies in downtown Florence in the Borgo Ognissanti area which will be easier to get to when you pick up the car as well as when dropping off as the SMN train station is just a few blocks away.
Read our tips about car rental here:
http://www.visitflorence.com/florence-car-rental/
For places to stay in Chianti, browse through here - anything you like, it is a very central area and not that big - you will not be far from anything:
http://www.tuscanyaccommodation.com/chianti/
For Florence, you could consider a small 2 bedroom apartment to share or a small B&B - take a look here:
http://www.florenceaccommodation.com/
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