I bareboated in both Croatia and Greece. Croatia was pretty lax on the rules. Maybe because I was living in the EU at the time, Greece required an EU ICC (pleasure craft operator cert). It is best to ask the operators on the requirements. They want your business and they have "ways" to deal with the required paper work
The charter company in Croatia "Sail Croatia" was crap. They specialized in flotillas, which they did not tell me. They sold my contract through two different charter companies and we didn't realize it until we got there. In Greece we used "Sailing In Blue" and they were excellent.
Cruising grounds. In Croatia we sailed Kornati reserve, that was fun! Nice wind, pretty easy. It is fairly remote so some may not like it. Typically many sail out of Split and go Island hopping through the more populated islands.
In Greece we sailed the Cyclades Islands, one way charter from Athens to Paros. That was fantastic! The Cyclades requires a fair amount of experience though. They can have a pile of wind and huge seas. I might suggest western Greece in the Ionian Sea.
In both cases I would suggest late May and June for your trip. July and August get really crowded. The winds are also huge during July and August.
For your first time bareboating I might even suggest the BVI as it is dead simple and there is significant support. I might also suggest getting a captain to help out on the first couple of days. It would take the stress out.