The Duomo is breathtaking, the restaurants on its piazza are tourist traps. Walk 5 min to Mercato Centrale or Oltrarno.
Better options: Trattoria Cammillo, Il Latini, Cibreo Trattoria, Trattoria Sostanza, Trattoria Mario (lunch only).
Oltrarno (south of the river) has the most authentic local restaurants — Trattoria 4 Leoni, Il Santo Bevitore, Vico del Carmine.