Excellent hot weather, school holidays though so heaving with visitors from early July, and also a bit more expensive due to this. Yo'd have to fly to Greece. Mid June would be better, or September if you don't like crowds so much or spending more money.Edited: 02 December 2017, 17:03
It should be very nice beach weather beginning of July. 10 days for 2 countries is not enough let alone just for Croatia IMO. You are not allowing time to really experience either one. Personally I would pick just one and enjoy your 10 days.
Also agree with picking one of those places!
There is typically direct flight service from Dubrovnik to Athens so if you plan it out well you could do half and half. But if you just stick to Dubrovnik you will miss a lot of great things around the country so it may be good to focus and see more of one country for this trip and come back and do the second country a different time.