You may see St. Patricks Co-Cathedral across town before you actually find this incredible building. Rest a while inside if it's open or just take in the facade from the street.
You'll have sightseeing choices galore when in Billings. St. Patrick's Co-Cathedral is a good place to start here, but there are loads of other fine places to discover. Reef Indoor Water Park, MetraPark, and First Interstate Arena are not far from the principal church and and will cap off your day nicely.