There’s a lot to see in Korcula, going well beyond the popular Korcula Old Town. That means you’ll ideally want at least three days, the first in and around the historic center, taking in the view from St. Mark’s Cathedral, visiting the town museum, picking up souvenirs and gifts, and sampling various eateries. The next day, you might rent a bike for a self-guided tour to Lumbarda or just pedal around the island. On your third, spend the day at one of the many beautiful beaches. A week will allow you to do all of that with time to relax in between.