Whatever the religion or whoever they're devoted to, shrines have a way of making you contemplative. Check out Izumo Shrine and share a silent moment with the local faithful.
You're spoiled for sightseeing choice when spending time in Iruma. Izumo Shrine is a good place to start here, but there are plenty of other interesting spots to explore. Belluna Dome, Seibuen Amusement Park, and Sayama Ski Area are close to the sacred place and will top off your day nicely.