Florence is a great starting point and base for a tour of Tuscany. Attractive day trips include Pisa, Lucca, San Gimignano, Arezzo, Fiesole, Lucignano, Siena, and of course the wine zone of Chianti. Greve in Chianti is the market town of the Chianti zone and it is in the hills surrounding Greve that you can rent a B&B room or a small apartment on a working vineyard for less than a hotel in Florence. The SITA Pullman buses take you to Greve and Panzano in about an hour. From then on you see few cars and many cypress and olive trees.
The SITA bus station is just west of the train station in Florence. This is where to go to catch a bus to Siena, San Gimignano, and so on. If you're at the roundabout, facing the train station, go 90 degrees left and stay on the left until just past the fork. You will see the entrance to the SITA garage on your right.
If you are to visit one place in Florence, it has to be the Piazzale Michelangelo. It offers an amazing view of the city. There is a lovely walking trail and even a large church, San Miniato, at the top of the mountain. It is a must see.
Fiesole is in the hills above Florence, only a short bus ride away from the center. It offers a beautiful view of the sunset, and a small museum located on ancient Roman and Etruscan ruins of a temple and an ampitheater.
World War II Florence American Cemetery and Memorial (http://www.abmc.gov/cemet...): 12 km 7.5 miles south of Florence on the west side of Via Cassia. The Rome-Milan highway passes near the cemetery. Open daily except for 25 December and 1 January; 9AM-5PM. The cemetery is the final resting place for 4,402 American military dead lost during after the capture of Rome and the battle for the Apennines. A monument is inscribed with the names of 1,409 Americans whose remains were never found or identified. The atrium of the chapel contains marble maps of World War II Italy campaign. 20 min bus ride from the Sita Station, just ask agent get a return ticket. Free to enter.
Biking options outside of the city include the Chianti area, where you can fully enjoy the hills and the elegance of the landscape surrounding you, which has been taken care of endlessly through centuries. Strong scents can be enjoyed in Spring. The warm temperatures and usually stable weather in the good seasons can make the ride even more enjoyable. If you feel more energetic, ascents to Vallombrosa from Pontassieve through Tosi can be very enjoyable. You start from the Arno river plain and you end up in a thick, shady, fresh forest. In all cases, avoid the hottest hours in Summer and be aware of the traffic, which can be heavy and not cyclist-savvy, until you get in secondary or less populated roads.