After reading this thread and checking it out by walking around earlier this month, we settled on Orhan. We walked by others, including Proto (a bit, er, "rustic" and not very inviting IMO.)

To get there, we followed hhonorman's easy directions, walked through old town and out the Pile Gate, looked left to see the expensive, overblown (IMO) and exceedingly crowded Nautica and saw the alley-sized street behind and leading downward toward the baylet and in the direction of the Tower Lovrjenac, marked Svetog Durda, leading into Od Tabakarije. You will see Atlas travel agency and the lower back entrance to Nautica, proceed downward toward the water (where there is often a renter of kayaks, etc. at the intersection with the concrete groin extending into the baylet.) Look straight ahead, you will see Orhan (which also has some apartments / rooms to let.)

Link to Google map to Orhan.

The staff were very accommodating, the selection and variety of food and wines really good, prices moderate. Orhan was a treat - we'd return in a heartbeat. I heartily recommend Orhan to anyone seeking a nice, pleasant, relaxed place to eat in Dubrovnik - the spectacular views, good service and food are most enjoyable!