Unless things have changed drastically, you won't get any beer other than Moretti or Peroni in & around the bars the Palazzo Vecchio or the Duomo (and you'll be paying extra for sipping in those surroundings) but if you go off the beaten track slightly the worst thing that you'll have to put up with is cheap, highly drinkable Chianti.
There were certainly a few places south of the Arno but i did find a place or two east of the Uffizi/Palazzo Vecchio towards the Bargello. Again, small winding streets that i can't remember, and even if you don't find them, you'll enjoy the experience. If you're there for a few days, book tickets in advance for the Uffizi- saves a load of time, and do make room for the Bargello. The Cathedral (with Brunellsechi's dome) is best viewed from outside- or ideally get a bus to the southside of the city and Piazzale Michaelangelo for views across the city.
I know that wasn't strictly beer related and apologise in advance <!-- s:lol: --><img src="{SMILIES_PATH}/icon_lol.gif" alt="

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