Location, location, location! The #10 bus is very close and runs frequently to San Marco; from there, you can easily walk to the Duomo and then to the Uffizi, Ponte Vecchio, and anywhere else in the center. The only thing better would be staying directly in the center, which of course comes at a price.
Miriam's apartment was perfect for me and my nephew; the fold-out couch gave us both some privacy. The place has plenty of room for two or even three people; it is nicely decorated, and has everything you need (kitchen with dishwasher, sizeable fridge, heated bathroom). The terrace is also lovely and would be a great place to sit in the warmer months.
Miriam was absolutely prompt for both check-in and check-out; she gave us a warm welcome, and her printed guidebook was much appreciated!