We spent the last days of 2012 at Francesca's. It was wonderfull!
The flat is cosy, clean, well equipped. We've been welcomed by Rosa who is a very lady.
The neighborhood is perfect : authentic with nice shops, trattoria, bars etc. It's very close to the historical center, few minutes walk from palazzo Pitti.
The only slightly negative point is that there is not a lot sunlight inside the flat, but the is because we went during winter when days are very short.
In conclusion we really recommend Francesca's appartment