Whatever the faith or whoever they're devoted to, shrines have a way of making you contemplative. Check out Hermitage of the White Friars and share a moment of silence with the faithful.
You're spoiled for sightseeing choice in Cupramontana. Hermitage of the White Friars is a good place to kick off here, but there are many other fine places to check out. Lago di Cingoli, Abbey of Sant'Elena, and Colonnara are close to the sacred place and and will cap off your day nicely.