The Franciscan monastery of Our Lady of Angels (Gospa od Anđela) sits on a low pine-covered peninsula just east of Viganj, halfway to Orebić. The cloister is small and exceptionally calm — a single low courtyard with a wellhead and a ring of squat columns — and the church behind it holds the painted altarpiece for which the monastery is best known, plus a small lapidary collection of sailors' votive offerings.
The walk along the coast road from Viganj takes about twenty-five minutes and is the obvious land-bound thing to do on a no-wind day. The cypress-shaded benches outside the church make a good spot to watch the Korčula ferries crossing the channel. Open daily; admission free, donations welcome.