You could visit Dubrovnik (give it at least 1.5 days, more if you use it as a base for Montenegro or Mljet or other islands); Split and/or Trogir (I loved Split's energy and could easily see enjoying a day or two there, others spend a few hours and are ready to leave; tiny Trogir is well worth at least a few hours to admire its medieval stone carvings); and - depending on the ferry schedules -- Hvar and/or Korcula (Hvar is much more upscale).

There are lots of threads on this board with information that might prove useful - you can use the search option at the upper right of your screen.

Croatia is beautiful - enjoy!

I agree wtih everything that was said by kja. I would not stay in Dubrovnik centre as it is very expensive. Stay in Cavtat which is gorgeous in its own right, and close to the airport. Easy to get to Dubrovnik from there and has tours to other islands from the port.

I am bias and love Korcuia. Hvar is beautiful but also expensive and you are limited to where you can stay outside of Hvar as there are not small towns near by. On Korcula you have a vast selection of small town throughout the island. Lumbarda is great and has beaches.

Whatever you do and wherever you go you will love Croatia.
Have a super time!

MidAugust is high season, so I would start looking for accommodations very far in advance. I agree with the others, and while I would try Korcula first, I would not rule out Hvar entirely but I would consider staying in Stari Grad since it is August (not sure if that will make a big difference or not).

Before flying out of Split,you should spend a night or 2 on Trogir,an island jut across the causeway.It is a most amazing place.Hvar town has a marble main square you will never forget.Elsewhere on this site are suggestions for some great seafood restaurants on Hvar....and wonderful pizza in Split....Split is essential.

Here is my trip report from the 8 day trip we took to Croatia (started in Rome, actually we did the Amalfi Coast before that). It was wonderful and I would not change anything. We stayed in old town of Dubrovnik and it was not expensive. Dubrovnik is very crowded during summer and the only time it was enjoyable to be there was evening and early morning so staying in the old town was important. It's a gorgeous place, but it gets a lot of cruise ship travelers so the mid day crowds were pretty huge. By staying there four days, and staying in the old town we got to experience it with less crowds, and we did day trips away midday.

Scroll about halfway down the trip report to get to the start of the Croatia part. I give contact information for the places we stayed.