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.
Updates
This sounds like the Konoba Kamenica - in the market square. It is the best place to eat the oysters which come from Ston on the Peljesac peninsula and are called Kamenice in Croatian! The place is Restaurant Peskarija. I'd recommend grabbing a table around 6pm, armed with book/iPod/etc. Make a beer last until you are ready to eat, and then enjoy watching the queue that you've avoided! Everything on the simple menu is excellent - try the mussels.
Send your feedback or queries to been.there@guardian.co.uk
Search Been there
