1 Night in Hvar and 1 Night in Korcula

If departing from Split, you might consider a morning catamaran to Hvar and then a late afternoon catamaran onward to Korcula. That would allow ample time to explore Hvar town while avoiding a 1-night hotel stay. Check both the Jadrolinija and Krilo websites to find a combination of sailing times that works. Note that some Jadrolinija catamarans only stop at Vela Luka, which is at the opposite end of the island from Korcula town.

I am going to Hvar just for the day. How much time is enough to see everything? There is a catamaran leaving Split at 7:45 am and the next one at 9:15 am. I will be departing Hvar at 5:45 pm to Korcula. So the early catamaran gives me 8 hours on Hvar (9 am - 5 pm) and the 9:15 am catamaran allows about 6 1/2 hours (10:30 - 5 pm). I plan on hiking up to the Fortress above Hvar, seeing the old town sites, eating, etc. It looks like some of the sites are closed in the afternoon. Thanks.

Hvar town is relatively small and it wasn't a tremendously long walk up to the fortress, so I think you could comfortably see the highlights and eat lunch in 6.5 hours. If many of the places you want to visit are only open in the morning, then take the earlier catamaran. You'll have no trouble filling the extra 1.5 hours, even if all you do is relax over a cold drink and people watch.