For tourists, the historical center of Athens (Old Town) is of interest first of all, where you will find the Acropolis hill with the Parthenon temple and a number of other ancient buildings, as well as Lycabetus hill with the church of St. George on the top (from here you can enjoy a beautiful view of the city).
Also check out the Plaka neighborhood, the oldest in Athens. In addition to museums, it is famous for its restaurants and boutiques. The gourmet's path lies on Kolonaki Square, where many restaurants and cafes are concentrated. For souvenirs, head to the Monastiraki district, where a noisy and colorful market unfolds on Sundays.
Good news for those who like to walk through museums - there are more than 250 of them in Athens! It is worth visiting the National Archaeological Museum with the richest collection of ancient art, the Museum of Ceramics, the Museum of Greek Folk Art, the Museum of Greek Costume.
In Greek restaurants you should try souvlaki (kebab), moussaka (eggplant casserole), tzatziki (yogurt sauce with herbs and garlic), homemade sausage... And remember that the portions in most taverns are huge! The perfect end to your meal is Greek wine (e.g. "retsina" - a white wine with a characteristic tar flavor).