My wife and I stayed in this apartment within the walls of the old town in June. It was quite expensive but is a very pleasant apartment in a great location. Our only gripe is that there is no kettle or toaster (although you can of course boil water in a saucepan on the stovetop).
The landlord is friendly and helpful. Dubrovnik is stunning.
Note that neither Dubrovnik nor especially this apartment is friendly for non-mobile people: lots of steps. more