Hvar or Korcula or both?

Hey guys! This may be repetitive but still would appreciate suggestions!
I am going to Croatia this October with my husband. We are going to be there for 8 days and 8 nights. Will land in Dubrovnik on 2nd at 8:00 PM. We want to spend 3/4 days in Dubrovnik either at the start or in the end as we leave on 9th evening from Dubrovnik itself. And want to split rest of the day's between Split and either of the two islands.
We both love to exploring the architecture and also like what nature has to offer. Love to party as well as relax and unwind at the beaches. If road trip to the islands is a better option, we don't mind renting a car as well.
Please suggest the best way to plan my trip. Also I am a vegetarian so would appreciate if you can drop in the information about where to get good vegetarian food in the above places.