We spent a day in Hvar Town last September, and we loved it! It was one of the highlights of our trip. We took the catamaran from Split. Trip takes one hour. Very easy to do from Split and you don’t need a guide.
We spent 4 nights in Split, too. Basically Had 3 full days. We also visited Trogir for about 3/4 of a day. It’s another easy trip from Split. If you are interested, we hired Maja Benzon, recommended by Rick, for a private guided tour of Old Town Split and Diocletian’s Palace. She was excellent! Very informative and interesting tour. We loved Split!
You could spend a night or two on Hvar if you want more time on the islands. Korcula is more logical to visit from Dubrovnik.