Just returned from a month-long stay in Antonella's apartment. It has everything you need; we bought fresh food at the St. Ambrogio Market, cooked it in the kitchen, and ate it on the terrace, which is amazing in the spring when it's lined with fragrant flowers. Antonella was welcoming and helpful and answered my few texts immediately. The bed is very comfortable, choice of bedding for hot or cold nights, and we had both in the April-May period. Heat and air conditioning (YES! the apartment has AIR now) both work quickly and quietly.
The apartment is on the "first" floor, called the second floor in north america, to be clear, there are 18 steps, that's all. It's quiet and private, even when they were fixing the street at the front of the building, it was still quiet at the back where we were.
The location is just off the right hand edge of most tourist maps (they tend to cut off at Piazza St. Croce), which is just about ideal, 10-15 minutes from the Uffizi, 20 from Il Duomo, away from the huge crowds but still near the centre of everything.