Claudio's place was excellent. The location is easily within 15 minutes walking from every major site in Florence, and only three to five to the Bargello or Duomo. The view of the Duomo is amazing! The neighborhood has excellent restaurant and gelato choices. It's close to the bar scene if you want it, but far enough away to be quiet at night.
Claudio and his friend Ranieri (who met us when we checked in) were extremely responsive and helpful. We had trouble getting the door open on the first night and Ranieri was there in 15 minutes to help. Turns out it was user error and he was very gracious.
The apartment was very comfortable. The air conditioning was an oasis during the hot July days. Other reviewers notes are correct - there are many stairs (we counted around 90) and the last flight is an old spiral. Not a big deal, but be aware. The bedroom ceiling is the roof. I could walk upright on the left side (I'm 5'11") but has to crouch on the right side. The rest of the apartments has normal ceilings, and that's where we spent out time anyway. It's roomy and well-furnished.
It's a great place to experience Florence. I highly recommend it!