We always stay at the Hotel Peristil in Split. We have stayed there about 4x over the past few years and recommend it to friends. It is family owned and inside the walls of the palace. They provide breakfast and have a lovely restaurant for dinner.
In Korčula’s old town there are two hotels right off the top of my head. Hotel Fabris (we stayed here once. Nice location but small rooms). The other is Aminess Korcula Heritage Hotel. We never stayed there cause they are always booked.
Just an FYI about korčula. Many of the people who rent out rooms or their houses within the old town use booking.com. They use this platform because they might only have 2+ rooms to rent and managing their own website is difficult or more costly. We know cause my husband’s cousin was renting out rooms this way. They aren’t any more because of illness.
We still haven’t made it to Hvar after more than a dozen trips down that way. We’ll be in Croatia the end of the month but will still not make it there. Maybe in 2026.