Hi Corinne and welcome to the DT forum! Your trip to Tuscany is coming up fast so I'll try to give you some ideas for your stay.
The Lunigiana, as is called the geographical area where Fivizzano is located, and the nearby Garfagnana are two really beautiful areas of Tuscany. These territories are dominated by nature and, if you like quiet and natural places, you'll definitively love them!
The luxuriant nature of the Apuan Alps, between the Massa Carrara and Lucca provinces, is the perfect setting for walking and hiking lovers. You can find a lot of interesting trails of every difficulty level and length. I found a few suggested itineraries here
http://www.parks.it/parco.alpi.apuane/ - and don't forget to buy a detailed map of the mountain and check the weather forecast before setting off!
The Lunigiana and Garfagnana areas both have characteristic tiny villages to visit, such as Fosdinovo, Aulla, Barga and Castelnuovo Garfagnagna. You' ll find some information and photos of the villages and main sights in the
official tourism board and here
http://www.ingarfagnana.com/
I think a great experience would be visit the Grotta del Vento - Wind Cave in Fornovalasco. This impressive grotto has Karst origins and can be visited in 3 guided itineraries that vary by length and time, from an hour to 2 hours. Read a recent article of a visit to the Grotta del Vento to learn more and see some pictures
http://www.discovertuscany.com/garfagnana/grotta-del-vento.html .
From Fivizzano, you can also easily reach the coast and enjoy the beautiful Italian seaside! Within Tuscany you'll find Forte dei Marmi, an elegant seaside town, Viareggio and Camaiore which all offer sandy beaches perfect for swimming.
The Ligurian region is very close and offers marvellous towns such as Portovenere, Lerici and the famous Cinque Terre (Monterosso, Vernazza, Corniglia, Manarola, Riomaggiore) . The Cinque Terre are connected by a beautiful trekking itinerary . Here you can read more about trekking another recent trip at the
Cinque Terre here:
A weekend at the Cinque Terre .
Hope these suggestions are useful!