We just returned 2 weeks ago & had an amazing meal at Nautika - right to the right of the main city gate entrance. Ask for a table on the terrace - the castle is lit up above you, the sea crashing below - absolutely spectacular! Food was very good - my husband had the broiled lobster - very very expensive, but probably among the best we've ever had (the lobster medallions I ordered weren't nearly as exciting...), escargot good, nice wine list & excellent service, but it's the setting that will blow you away.
In the old town, Rosarij at the far end of the 'restaurant street' that parallels the Placa, was very good. Hope you love this town as much as we did!