I loved Laura's apt! I was there for about 5 weeks and I couldn't have picked a better spot. It's much bigger than the pictures show, it's fully renovated and airy -- I liked having a LR and dining area. The courtyard was such a nice treat too, to be outside!
It is about a 15 minute walk into the center, but I personally didn't mind that, it's a nice walk and you're removed from the chaos of the center. It also has several bus stops near by that you can use to go to some of the other parts on the other side of the Arno, easy bus ride to the train station too -- I never had trouble finding a bus near where I was to get home, if I didn't want to walk. It's in a nice area with pretty squares/parks nearby and you can almost always find an electric bike outside if you'll be using them during your stay!