The Danish knight, Erik Axelson began the building of St. Olaf's Castle in 1475. It's location on a steep, rocky island in a fast moving river was chosen with defense in mind, as the castle was built on what was then the Swedish/Russian border. The Russians claimed the castle was part of a land grab, was built on their side of the border and tried to interrupt the work. The castle changed hands several times until 1917 when Finland became an independent nation. It was thoroughly restored between 1961 and 1975 and is now one of the best preserved medieval castles in the Nordic countries.
If you enjoy the performing arts then Savonlinna is for you. The Ballet Festival begins in mid June and after a short break the Opera Festival takes over. In all, almost 8 weeks of performances. If your tastes run to something a bit more participatory remember the words of the Bard, "All the world's a stage and all the men and women merely players" and take it as your cue to star in your own drama. Activities from hiking to camping to canoe trips are all available as are cruises on the lake, or you could rent a car and write your own script.