Camares Cafe (tel. 22890/28-570), on Mavroyenous (Taxi) Square, has light meals and a fine view of the harbor from its terrace. It's open 24 hours and, for Mykonos, is very reasonably priced. Try the striftopita or crispy fried xinotiro (bitter cheese) and the thyme-scented grilled lamb chops (9am-2am; no credit cards). As is usual on the islands, most of the harborside tavernas are expensive and mediocre, although Kounelas, on the harbor (no phone; no credit cards), is still a good value for fresh fish -- as attested to by the presence of locals dining here.
Restaurants come and go here, so check with other travelers or locals as to what's just opened and is getting good reviews.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.