You may spot Sankta Maria kyrka in the skyline before you actually find this grand building. Rest a while inside if the doors are open or just appreciate the facade from outside.
This principal church is free to enter, which is wonderful news if you're watching your budget. Sankta Maria kyrka is located in Innerstaden. When you're finished, DBWs Botanical Garden, Gotlands Art Museum and Visby Ringmur are close by and also worth a look.