I organize my sightseeing geographically and do it all on foot. So this is what I suggest you: walk a lot. Florence buses dont cover the old centre very well.
Of the many bus lines, I think that the most value for sightseeing are: lines # 7, 10, 12, 13, 31 and 32 which connect the train station with the Piazza San Marco through Piazza Indipendenza. Bus #7 continuoes on to the Piazza della Libertà and then on to Fiesole.
Lines #12 and #13 go from the train station to Porta Romana, up to San Miniato Church and Piazzale Michelangelo, and on to Santa Croce Church.
Here you have a map will all the bus lines. I find it very useful.
Fun little elettrico minubuses wind through the old centre of the town and up and down the river. Line A gets around the centre from the train station to Piazza Beccaria, Line B goes up and down the Arno river from Borgo Ognissanti to Santa Croce Church while Line D goes from the train station to Ponte Vecchio (Old Bridge), cruising through the Oltrarno neighborhood and finishing at Ponte San Niccolò. You'll be sitting with local seniors in this buses.
I suggest to buy ticets at the bars, the tabacchi shops, newsstands or at the train station bus stop, €1,20 for 90 minutes, €4,50/4 tickets, €5,00/daily, €10,00/12 tickets, €20,00/25 tickets, €12,00/ 3 days ticket. As you get on the bus you have to validate your ticket in the machine onboard. Tickets bought on board costs €2,oo for 90minutes. Usually you board at front or rear doors and exit from the central doors.
Hop-on, hop-off bus tours generally stops at major sights. Around town you will see this big double-decker sightseeing buses near major sights. Tourists on the top deck can listen to brief recorded descriptions of the attractions, snap photos, and enjoy the drive-by-look.
Tickets costs €20,00 for 24h, firs bus at 9.30 am and last bus at 6.00pm . Pay as you're on board, tickets include two bus lines - Blue is one hour with a trip up to the Piazzale Michelangelo, Green is 2 hours with a side trip to Fiesole. For more informations visit
http://www.firenze.city-sightseeing.it/ As the name says, you can hop off when you want and get on the nex bus (every 30 minutes). Hop-on stops include the train station, the Duomo, Pitti Palace, Santa Croce, Piazzale Michelangelo, Fiesole and many other sights.
As more sights are situated in the old city center this big buses can't go, so before look at the route map.
You may find this a funny thing but I find this very useful: In Florence You can buy tickets with an simple SMS from your mobile phone send a text message with writen "Ataf" at this number +39 339 9941264 and you will recieve an electronic ticket to show to the ticket inspector. The cost of the ticket is €1,20 for 90 minutes + the cost of the text message depending on your mobile phone operator. To do this you have to ger registerd to
http://www.bemoov.it/ and give a credit card number from where the Florentine buses company will charge the cost of your ticket. For more informations check the buses company website
http://www.ataf.net/ or call the toll free number 800-424500 (from fixed lines) or the payment number
199-104245 (from mobile phones).
Also I find it very useful to know the exact time the bus will come at the bus stup. You just have to send an SMS to +39 3424112512 with the number of the bus and the bus stop code (you will find it at the bus stop sign). For more information visit www.temporealeataf.it .
