Whatever the belief system or whoever they're devoted to, shrines have a way of making you contemplative. Visit Mefu Shrine and share a quiet moment with the local faithful.
You'll soon find out why this Matsue Shinjiko Onsen sacred place is visited by many travelers. If you're looking for other things to keep you busy, Tamatsukuri Hot Spring, Matsue Castle, and Lake Shinji are in this area as well. They won't take you long to get to from Mefu Shrine.