Sounds like a great trip ;-)
We did a loop this year around Bologna (posted in another thread recently) that involved a visit to a balsamic vinegar production site (Acetaia Villa San Donnino, Via Medicine, 41126 San Vito di Spilamberto) and a parmesan cheese site (Latteria Sociale La Grande, Via F Rosselli 41, Reggio Nell’Emilia) that might fit in your driving plans. A friend of mine and I also did the visit to the the Ferrari museum in Bologna. Both the production places require reservations with nominal fees (true cost comes in the sales shops at the end).
For Florence, we always make a trip up just to enjoy a few small things -- Vestri Chocolates, Borgo degli Albizi, 11R (really is worth it to enjoy the selections on the shelves) and Aqua Flor, Borgo Santa Croce, 6 (comfortable leather chairs in the display area for me; lots of fragrances and scented items for more enthusiastically involved husbands than I and wives to buy for selves and as gifts). Also easy to overlook the Museo del'Opera del Duomo behind the apse of the Duomo, but some beautiful work in there (BTW, if you go to the Sforza Castel in Milan and the Museo del'Opera in Florence, you will add more of Michelangelo's Pietas to your list). The small town of Empoli is just outside Florence and has some beautiful scenery plus a great Etruscan museum.
Pauline mentioned above Santa Margherita Ligure. There is a fantastic stretch of shoreline with a very nicely laid out walking path that goes from Rapallo to Santa Margherita Ligure, Portofino, and on to San Fruttoso. You can take a water ferry to any of the stops and walk the short hops between each town and treat yourselves to beer/wine and snacks as a reward. Rapallo is the bigger of the towns and has a nice waterfront area with hotels and restaurants. Portofino is a good place to watch the people coming off their yachts.
For Lucca, always recommend climbing the Guinigi Tower to see the city from above and renting bikes at Poli's (in Piazza Santa Maria) for the 2 1/2 mile ride around the city walls. Would suggest Trattoria Gigi and Ubaldo's for meals (Gigi's is near Guinigi Tower and Ubaldo's is immediately outside the amphitheater). Can provide more info if you do decide to go to Lucca -- always get carried away since we love the city so much.
Only bad thing about Italy is all the choices that have to be made between so many great places to go and fun things to do. My apologies for rambling on -- Enjoy!!