We had our first meal in Hvar at Pizza Kogo, a relaxed little cafe that serves terrific pizza and pasta along with traditional Croatian seafood and salads. The restaurant's outdoor dining area is located right on Hvar Town's main square, Trg Sveti Stjepana, and has great views of Sveti Stjepan Cathedral which is just a few steps away. From your table, you also have a view of Spanjol Fortress on the hill above the town.
We had a very good lunch of margarita pizza, traditional cabbage salads, and a side order of local marinated olives. We had the good fortune of meeting two very nice British gentlemen at the table next to us - they said their pasta dishes were excellent.
The service was very good - the waiters were friendly and they encouraged us to hang out at our table long after our meal was finished. The beer selection was good, and I was able to get delicious apricot nectar as well.