Frascati, Castelli Romani, Cesanese — the wines from hills around Rome are crisp, mineral, and pair beautifully with Roman food.
Don't order Tuscan Chianti out of habit. Ask for 'un vino locale' (a local wine) and the server will guide you.
For reds, try Cesanese del Piglio. For sparkling, Cannellino di Frascati.