Thanks flirtinfilly, I saw this restaurant in Travel and Leisure, too. - we'll check it out.

And no worries annhig- I think I added an "i" to your name accidentally as well!

Zio Gigi: Small place, lots of locals, not fancy. Near the Duomo.
Buca dell'Orafo: I think the tourists have discovered this place, because the prices have gone up lately. Still, pretty good. It's under an arch near the Ponte Vecchio.