Grotta del Vento, The Wind Cave
North of Lucca, in the area known as the Garfagnana, is the Grotta del Vento - one of the most accessible (and highly commercialized!) caves in Tuscany. As a day trip from Florence with kids, it is pushing the limit - we followed the directions on the official website, which had us getting off the main highway much earlier than Lucca, and it was slow and tedious going trying to stay on the correct roads. I would suggest you stay on the A11 until Lucca and then get on the SS12 heading north up the Serchio River Valley.
The trip is nearly two hours, but once you are past Lucca and start heading up the valley, it is really quite picturesque. You also pass the Devil's Bridge at Borgo a Mozzano which is an amazing example of medieval engineering and worth a trip in itself. Either before or after a visit to the cave, you can also stop in Barga (barganews.com is a good website), a beautiful and ancient hill town with the ruins of a Roman aqueduct among its sights.
The drive from the main road up the side valley to the cave is stunning - there are a couple of small dams along the way, with deep blue pools of water, and some amazing mountain scenery. The Grotta del Vento has to be visited with one of their guides, and there are 1, 2, and 3 hour itineraries - definitely visit their website for up to date information. Some sites I read said they were closed in the winter, but that is not the case - they are open every day except for a couple of major holidays. The cave has thousands of stalactites and stalagmites, and has built in steps, ladders, and lights (at least on all the parts we were on during the one hour tour). The guides speak several languages, and since it was just us we took the tour in English. One of the coolest parts of the visit was when we were at the deepest part of our tour and she turned all the lights off - it is truly devoid of light.
While I would not put this side trip on my list if you only have a couple of days in Tuscany or it is your first time visiting the area - if you are a nature lover and/or have kids, this trip can be a lot of fun. I would say it is not for serious spelunkers - it is a tourist attraction, and not a cave you can explore on your own.