Whether you'd like to pay your respects or learn more about the history of the building, Roman Catholic Church of Immaculate Conception of the Blessed Virgin Mary is an interesting site to explore. Check to see if this sanctuary is publicly accessible to experience the calmness it offers inside.
When you've finished at this Tartu house of prayer, why not check out Student's Lock-Up, Tartu Town Hall, and University of Tartu? They're not very far from Roman Catholic Church of Immaculate Conception of the Blessed Virgin Mary and also a favorite with travelers.