You needn't have a strong religious faith to enjoy the peaceful atmosphere of Torshavn Cathedral. Look up when the next service is scheduled or when you can go for a wander through.
When you've spent a bit of time at this principal church in Torshavn, why not make your way to The Nordic House, St Magnus Cathedral, and The National Museum of the Faroe Islands? They're close to Torshavn Cathedral and also popular with many tourists.