Koguva, 6km off the main road on the western tip of Muhu, is an exceptionally well-preserved, old-fashioned island village, now protected as an open-air museum. One ticket allows you to wander through an old schoolhouse, a house displaying beautiful traditional textiles from the area (including painstakingly detailed folk costumes) and a farm which was the ancestral home of author Juhan Smuul (1922–71). You can poke around various farm buildings, one of which contains a collection of Singer sewing machines.
The village is still very much lived in, mainly by families that have resided here for generations, so respect their privacy by sticking to the designated museum areas.