We rented a house in the old town and the owner recommended the little restaurant in the harbour. I can't remember the name but it's through the wall around the corner from the palace where the launches leave from. The squid is great and the risotto, but you do need to get there early. Cheap and cheerful and a great place to people watch.
Keep an eye out for concerts in churches around town that are also interesting and easy to get to.
Taking buses to the main ferry port is also very simple and means you can take excursions to islands futher north. They leave from the north side, just outside the walled town.
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