For Florence, we ate at a sandwich place in San Lorenzo Market (see picture). They had really good tripe sandwich (only 3 euros in 11/2009).
For sit down place, we went to this really famous place called 'IL Latini' (see picture). They had good Florence steak. The problem is each steak is at least 1Kg (or 2.2 lbs)!
Another place our host recommended was 'Trattoria Quattro Leoni'. It is near the old bridge.