You are looking for some food that is not Italian. There are many places throughout Florence. Check them out. (Being Updated)
Brasilian
Brasileiro | cucina brasiliana a Firenze | FRESCO E PRONTO
Maracanà Grill – Ristorante brasiliano a Firenze – Cucina tradizionale brasiliana – un angolo di bra
Japanese
Kome is very good – they do Japanese and a bbq upstairs.
Ristorante Niwa | Cucina Giapponese e Thailandese
BUDDAKAN Firenze Piazza Santa Croce
KOKO Restaurant – Sushi Bar – Firenze
Persian
Darvish Cafè Firenze Persian Restaurant in Florence
Tai
Ristorante Niwa | Cucina Giapponese e Thailandese
Banki Ramen Real Ramen in Florence read about it here Via dei Banchi 14r, Firenze, Italy 50123, +39 055 213776
American/Steak houses/ Hamburgers
Cafè Deluxeè Piazza Indipendenza ang. Via XXVII Aprile
Lebanese
Firenze Moms 4 Moms Network 