The Pakleni Islands, just offshore from Hvar Town, are the obvious day trip — a short water-taxi ride out to Sveti Klement or Jerolim for swimming, naturism, and a long lunch at one of the konobas. Boats leave from the Hvar Town promenade roughly every half hour in summer.
Further afield, the island of Vis (the next island west, two hours by boat) is the off-the-beaten-track choice, with the Blue Cave on Biševo as the headline sight. Plenty of operators in Hvar Town run full-day sailing trips combining Vis, the Blue Cave, and a swim in the Pakleni Islands on the way back.
Inland, the village of Velo Grablje is an easy half-day on a hired scooter — abandoned mostly in the 1960s, recently brought back to life by a lavender festival every June.