A small car ferry runs frequently between Orebić (4 km east of Viganj) and Korčula town, taking about fifteen minutes to cross the channel. From Viganj it makes an obvious half-day trip: cycle or drive to Orebić, leave the car, and walk on as a foot passenger.
Korčula town is the medieval walled city traditionally claimed as Marco Polo's birthplace — a tight peninsula of stone houses, a fine Gothic-Renaissance cathedral, and the small house museum identified (somewhat speculatively) as Polo's family home. Allow three or four hours in Korčula plus the ferry time. The Moreška sword dance, performed weekly in summer, is worth timing your visit around.