There are many little hotels around the train station in Florence, but they're very likely to be expensive so you probably should look for one a few blocks away. If you don't have a reservation you can go to the information office at the train station and they will find a room for you in a hotel according to your budget and the room size & location you desire to find, and they only charge you 2-3 dollars for the service.
This is how I found a room for one night in the Hotel Esperanza, a very small hotel in a quiet and hidden street placed about 10-15 minutes (walk) away from the train station.
Unique Quality: This hotel is very modest, not luxurious at all, but the rooms are fairly big and the bathroom as well (there are rooms both with and without a private bathroom), and it's clean. It also has a very small dinning room where you can have breakfast. The street is quiet and very close from downtown.
The price for one night is approximately 70-80 american dollars (this was in 2000), in a double room with private bathroom.
Viale Michelangelo 1, Florence
Via dei Tornabuoni 1, Florence
Piazza Santa Maria Novella 7, Florence
Piazza Ognissanti 1, Florence
Latest Florence hotel reviews