That left Peppino's which is more expensive but appears to be much more a single specialty gelato place.
The Pistachio Premium certainly caught my eye with its thick murky green colour flowing from tart shells. The serve itself was unusual - there's the dark brown sludge on top with some bits of nuts, and this part has all the pistachio flavour. The pale green below was really quite plain and lacking. I enjoyed eating the sludge but not so the pale.
It is likely to be the better gelato place in Dubrovnik, but maybe that just means there isn't a particularly good one (yet)...