Check out the youth hostel - wait, I'll give details - called Ostello Archi Rossi, in Florence. I booked thru Hostelworld.com
I was there a few days ago and if you are on a budget . . . .
Location: it is a 5 minute walk from the train station and no steps (okay, a couple of curbs and 2 steps in the entrance, a lot of the rooms are one flight up, but I had a ground floor). The area was quiet at night and I felt safe coming back as late as 10 or 11 pm (woman alone). From the hostel, it's 10 to 20 minute walk to most of the major sights (Academia, Duomo, Uffizi).
Rooms: They have private rooms. I had a single with shared bath, but I think some of the doubles include a bath. The rooms have computers and free internet access. Mine had a sink. Everything was very clean and the rooms are spacious. I paid 36 euro a night.
Food: Breakfast is included. There is a large fridge for storing your own food (and wine). They sell a variety of snacks, frozen dinners and beverages at less than minimarket prices and they sell fairly tasty dinners every night except Sat. The dining room is a great place to meet others (ALL ages) and get up-to-date info on where to go and what to do.
General: All the staff I met (I was there 5 nights, so met pretty much everyone) were friendly, out-of-their-way helpful and spoke excellent English. There is a lovely courtyard garden that was almost always vacant. Everyone I talked with said it was the best hostel they'd encountered. The 11 pm to 7 am silence rule is pretty generally enforced. Before you leave, do your laundry - 3 euros each for large American washers & dryers and the detergent is free.