Biking Tuscany?

If you are a strong rider you can. Italy is not flat like Florida, it's mostly mountains and hills and some passes climb well over 2500 mts (8500 ft). If you ride like Lance Armstrong (or at least you dope like him) you can ride anywhere in Italy. Highways in the country side tend to have no shoulders or bike lanes, therefore keep to the right and be careful.

There are many bike-able roads in the hills of Tuscany, Umbria and Marche. You can also find flat routes in the plain of the Po and Puglia. Look for routes here: http://www.bikemap.net/en/regional/Italy/#gsc.tab=0 and I'm sure there are many more sites and Forums as there are a zillion bikers in Italy. I've talked to American bikers who say the Italian drivers are quite respectful of bikes. You might want to bring a helmet as I think rentals may not necessarily include one.

Tuscany is a place for hard core bicycle enthusiasts. Any such biker would usually take his own wheels on the plane. Most rental bikes are not up to my standards in bicycles. And Bike rentals in city centers like Amsterdam just rent junk bikes due to the high chance of theft.
You would be able to store a bike in a hotel or hostel--or they'd have a storage room.
Roads are well paved if a little crooked, and there are many back roads that are ride able. The area is very hilly, however.
The only two wheels I'd want to ride in Tuscany/Chianti would have a 750 cc or larger motor.

Tere are companies that give biking tours of Tuscany. One that I know of is Backroads. I don't have all the details, but people I've spoken to love these. Not for your casual biker, but you seem up to the task. You can google them.