A tiny village 6km southeast of the town of Korcula, Lumbarda boasts one of the only sandy beaches in the region (as opposed to the usual pebble beaches found elsewhere). The beach isn't huge and doesn't have many facilities. In my opinion, a day trip is time enough.
Likewise, we don't really associate Croatia and the Balkans with wine and olive oil. And I can confirm that Croatia produces excellent olive oils and also does pretty well on the wine front. You really should take the time to tour the groves and vineyards during your trip to the country.
Visiting a vineyard, taking part in a wine tasting and hanging out on the beach for a few hours are all fun activities you can enjoy in Lumbarda. Its best known wines are Grk (white) and Plavac Mali (red).