The Euro has become the standard currency through most of Europe, Italy and thus Florence.  It is important to note that under normal circumstances, the US$ notes, travelers cheques and even American Express Euro Cheques are not widely accepted as payment.  

If you are fortunate enough to find a bank that agrees to cash them you will need to pay 2-4% conversion fee which is certainly no bargain.  It is likely that use of local ATM (Cash) machines is the best method for you to obtain Euros while most of Europe, including Florence.  You could consult with your local bank about international ATM machine usage fees and expected exchange rate and commissions.  

Also, while credit card payment is widely accepted, its best to not to use American Express because most mechants will not want to pay the higher fee.  Visa and Mastercard are readily accepted throughout Europe.  Even Discover is quite popular but the best bet is to use a debit card associated with Mastercard.  The exchange rate will be minimal and at least half the ATM machines you find will honor the transaction.

Of course cash gives you the greatest advantage.  Europeans like to barter but don't even think about bartering with a credit card, it's insulting