We had a wonderful stay at Cosmea which is in a genuinely superb location, south of the Arno in a less-touristy, more 'genuine' area of the city (making for better food and drink, at far better prices), yet only a few minutes walk across the Ponte Vecchio right into the heart of the city. Moreover, the view from the roof terrace made you feel as if you were right in the center anyway, with a panoramic view of the skyline and a particularly close-up view of both the Duomo and the Palazzo Vecchio, with the Uffizi and river in the foreground and the hills in the background. (the photo here really doesn't do it justice!)
Diana and her colleague Francesca were both very helpful and responsive with any questions we had and were great at suggesting unusual places to visit, away from the tourists.
If I had to be 'balanced' by putting in a negative point, there are a large number of steep steps up to the apartment, which is a little tricky if you have oversized luggage, and the overall size of the apartment (particularly the bathroom and kitchen) is very small, so do not be expecting 'luxury'; Cosmea is really all about its location, which is spot on, and if you're spending most of your time eating out, this doesn't matter at all. Thank you Diana and Francesca.