Regarding the island part of your trip -- we have been to Hvar and Korcula, but our favorite was the tiny island of Vis, which you might want to consider. It will be less expensive and not so crowded as Hvar and Korcula.
Vis is accessible from Split via ferry every morning, and there's an early morning ferry from Vis back to Split -- you get off the ferry, walk across the street to the bus station and catch your bus to Dubrovnik.
Vis is a quiet little island with a big yacht harbor. The main town (Vis Town?) is where the ferries dock. Walk around the harbor and there's an area called Kut, which is slightly more picturesque. It's so small though that it doesn't really matter where you stay.
There's a gorgeous little fishing village on the other side of the island, called Komiza. From there you can take an excursion to a Blue Hole -- but go on a sunny day. The day we went it was cloudy and the blue wasn't so striking. Here's a link to a story about Vis.
Regarding Dubrovnik -- we obviously prefer quiet, uncrowded places. So on our two visits to the Dubrovnik area we actually stayed in Cavtat, another gorgeous little fishing village just south of Dubrovnik, near the Dubrovnik airport. You can take a bus or ferry into Dubrovnik to see the sights, but the benefit of doing this from Cavtat is (a) you can see the Dubrovnik harbor from Cavtat, and if it is filled with cruise ships, you know to put off your visit for another day -- and (b) you get to leave Dubrovnik and come back to peaceful Cavtat and watch the sunset from the harborside cafes. You can also take the Montenegro tour (highly recommended) from Cavtat. And when you're ready to leave, the airport is just a few minutes away.
EDIT: Here's a link to a timetable showing cruise ships in port in Dubrovnik in September 2015, which can be helpful in planning your stay in that area. You can change the date, port, etc. depending on your needs.