Best weather will be the Canaries or further south (Cape Verde, Gambia, Morocco) or the Eastern Med. The east has a lot less rain and much warmer temperatures on average than the Balearics into October (Mallorca gets ~12 days of rain in October on average whereas the Canary Isles gets 2-4 days and Cyprus gets ~2-3 days and the sea temperature in the Eastern Med will be ~25 deg C). I think you are right that the weather will start to break in Croatia and that area would be better to visit May-September.
In the Canaries, the islands are very dry and hence quite barren. Although Gran Canaria has some greenery inland and good walking / cycling. The tourism is very much focused around the beaches, water sports etc. If you want a bit of architecture or history, look at Turkey, Cyprus or the southern Greek islands.