Francesca's place near P. Michelangelo is superb. Only 20 minutes walk to the Ponte Vecchio, although guests of my age may prefer bus or taxi back, yet really peaceful. The only noises in the beautiful private garden in the evening were crickets and an owl - quite amazing for somewhere so close to the centre of Florence. The apartment its-self is stylishly decorated and furnished with all you could need for a stay in Florence. Lots of extra touches from Francesca, a truly perfect host, such as high quality soaps and shower gel; well stocked fridge and store cupboard; fresh fruit and flowers from Francesca's garden; wine and water.
I have no hesitation in recommending Francesca's place and would love to return myself - ideally before she realises that she could charge much more for such a fantastic experience.