Most Greek tavernas do not have a wide selection of desserts. They usually offer to customers that they like, some sort of free sweet or fruit after the meal. In summer this will be watermelon (karpouzi) and cantaloupe (pepponi). In winter many tavernas have Halva which is an interesting sweet made from sugar, farina, cinnamon and almonds.
Most Greeks, if they have a hankering for sweets will leave the taverna and go to a pastry shop or ice cream shop or combination of both. These are very popular and quite common and are called Zacharo-Plastea which I guess translates to sugar-design. Zacharo being sugar and Plastea being the root of our English word for plasticity. If you are named Zachary you better be a sweet person.
Anyway, once you get to a zacharo-plasteo, if its a good one, you will have a wide variety of sweets to choose from such as French or Viennese pastries and more traditional Greek sweets like Kataefi and Baklava. This photo, on the left, is from one of my favorite sweet shops which happens to be a chain and called Dodoni (hedonism). I recommend this chain to you. Some other well know sweet shops are Asimakopoulos, Leonidas, Luxor and Flocafe.