Awww Jerry, you make me blush

no genius at all, just glad to share the stuff I know from living here!
Knowing now about your feet, I'd recommend getting a taxi whenever the small buses won't work for you: you can have your hotel or B&B call it for you, then you'll find it right outside and it will take you the whole way.
But if you can do a little bit of walking and there's a bus you can catch in the direction you're headed, then by all means use them as they will be cheaper than taxis. A 90 minute ticket costs €1,20 which means you get on, put your ticket in the machine and have the time and date stamped on it - please do it because even if you get lucky and no one checks your ticket that one time, there are a lot of controls and the fine is high if you didn't stamp the ticket! In any case, if you need to catch another bus within those 90 minutes, you don't need a new ticket since the first one is still valid. So when you can, use the bus
In this case, I'd recommend taking
line D from the SMN train station. It is the one with the shortest walking distance for you: from Via Taddea, you should head to Via Nazionale and then on to the train station, the front short end is where bus D stops. It is about 650 meters total from Via Taddea according to Google maps. You should see the route on
this map (I hope) and the
timetables here. Bus D will drop you off right in front of
Palazzo Pitti
Since you're in the center,
this map of the 4 lines that cross the center will be of the most use to you. Line D is the green one - just follow the
arrows along the routes to determine where you'll find bus stops. Since many streets are one-way, the bus has different routes in each direction and you want to be at the right stop to head in the right direction. If they match, then the stops will be on one side or the other of the small streets. You can buy bus tickets from many
bars (coffee shops) and newsagents. There will be stickers on their doors or somewhere that says they sell ATAF tickets - you can buy 1 ticket that actually has 4 rides on it for €4,70 so you actually save a little bit for the 4 rides.
Hope all this extra info is useful to you and to others!! Let me know if you have any other questions - and hope you enjoy your time in Florence
