If you do end up going to the Greek place, here are some recommendations off its menu:
Appetizers
Gigantes - oven-baked giant beans with tomato sauce, olive oil & herbed feta
Dolmathes - grape leaves stuffed with rice, currants & pine nuts
Briami - traditional oven-baked summer vegetables with oregano & garlic
Soutzoukakia - grilled meatballs with tomato & green olive compote
Melitzanosalata, Tzatziki
Salads
Horiatiki - classic Greek salad of tomato, cucumber, bell pepper, onion, oregano, olives & feta
Main course
Psari Psito - traditional grilled whole fish with braised greens, lemon & Cretan olive oil or wood oven roasted with Greek olives, saffron potatoes & roasted tomatoes
Katsikaki Yuvetsi - stewed goat with orzo, tomato, spices, artichoke & feta
If you do decide on the goat, make sure it's fresh and not frozen. And remember to have a sip of Ouzo diluted in cold water as an aperitif.