While you could spend your entire vacation in Korčula and really enjoy it, it is also easy to check out some of the surrounding islands for more fun. Using Korčula as a headquarters, you could take a boat tour to islands such as Hvar, Mljet, Lastovo and Dubrovnik. You could also check out the Archipelago beaches or try out a fishing tour.
Mljet is a short trip from Korčula and you have various options of how to get there. If you are visiting during the summer you can take public transport. If you are visiting off season you could get a ferry over. During the off season, you can go online to register your ticket for the ferry from Korčula to Mljet. Between July and August you can purchase your ticket the day before you travel (recommended as they sometimes sell out) and take the passenger ferry over.
Once you are in Mljet you can hike the National Park. There are many beautiful natural things to see and you can also check out the Benedictine monastery that is on an island in one of the lakes of Mljet. Bring your scuba gear to check out the lakes!
Hvar is also easily accessible from Korčula. You can take the catamaran over and this boat operates all year. If you wanted to check out Split you can spend a layover night there en route to Hvar as the ferry makes stops there. Once in Hvar you can check out the gorgeous beaches and fun nightlife. Take a walk down the ancient streets of Stari Grad (built in 384 BCE) to soak in the history of the island.
Lastovo is reached by a foot passenger ferry that runs Tuesdays and Thursdays. This island is known for agriculture and has many vineyards and olive tree orchards. While in the city rent a bike to get around. You can also pay to go diving and see what enchanting discoveries you can make below water. You can hike the 200 km of trails the island has and sea views of the Adriatic sea and surrounding islands.