Eating in Cortona
Trattoria la Grotta, just off Piazza Repubblica, is a traditional, cave-like place with daily specials and an enthusiastic following (pastas-€7, meat-€8, Wed–Mon 12:00–14:30:00 & 19:00–22:00, closed Tue, Piazza Baldelli 3, tel. 0575-630-271).
La Locanda nel Loggiato serves up big portions of Tuscan cuisine on the loggia overlooking Piazza Repubblica. While they have fine indoor seating, I'd eat here only for the chance to gaze at the square over a meal (pastas-€7, meat-€7–15, Thu–Tue 12:15–15:00 & 19:15–23:00, closed Wed, Piazza Pescheria 3, tel. 0575-630-575).
Fufluns Tavern Pizzeria (that's the Etruscan name for Dionysus) is easy-going, friendly, and remarkably unpretentious for its location in the town center. It's popular with locals for its good, inexpensive Tuscan cooking and friendly staff (cheap, lots of pizzas but plenty more, good house wine, Wed-Mon 12:15-14:30 & 19:15-22:30, closed Tue, a block below Piazza Repubblica at Via Ghibellina 3, tel. 057-560-4140, run by Alessio and Simona).
Osteria del Teatro tries very hard to create an Old World atmosphere and does it well. It serves nicely presented and tasty Tuscan standards amid feminine, nostalgic elegance (closed Wed, 2 blocks uphill from the main square at Via Maffei 2, tel. 0575-630-556).
Enoteca la Saletta, dark and classy, is good for some fine wine and a light meal. You can sit inside surrounded by wine bottles or outside to people-watch on the town's main drag (Thu-Tue 7:30–24:00, closed Wed, Via Nazionale 26, tel. 057-560-3366).
For a Picnic: On the main square, the chic little grocery store, Enoteca Molesini, makes tasty sandwiches (see list on counter and order by number) and sells whatever you might want for a picnic (daily including Sun morning, Piazza della Repubblica 23). Munch your picnic across the square on the steps of City Hall, or just past Piazza Garibaldi in the public gardens behind San Domenico Church.