My favorite place is Dubrovnik and I think it should be on your list. There are so many other places worth a mention though and I don't think you can go wrong in picking just about anywhere. But other places that I have really enjoyed are Korcula, Vis, Brac, Split and Makarska.
It would be nice to know how long you will have though!
The word “best” means different things to different people. Really depends on your interests.
There are five main regions in Croatia - Istria, Kvaner, Inland Croatia (Zagreb), Dalmatia & Dubrovnik region.
In the Istia region the main airport is Pula which is Istria’s biggest city known for its Roman monuments and amphitheatre. Rovinj is one of the main resorts and has some beautiful scenery with red-roofed houses surrounded by sea on three sides. Porec is a lovely Roman town as well. Both Rovinj and Porec can be busy in the summer months. Inland Istria is much quieter with oak woods, vineyards and hilltop towns.