While Greece isn't know for it's wine, there are some drinkable ones. And when you add a view of the sea, you tend to forgive the bitterness of the white wine. Naxos actually has a couple of great spots to taste some vino in the city center. No need to drive to the country side and more importantly, drive back tipsy. No bueno wanderers!
A popular spot for locals and tourists alike, it's definitely one of the tastiest of all the local taverns. While it doesn't have a view like the restaurants that line the port, you won't miss it after you try their food.