Tallinn is the official capital of Estonia, but Estonians often say that the town of Tartu is the real heart of the country. Tallinn may be the political and financial center while Tartu has strong academical and cultural heritage.
Talking about history: the university of Tartu was founded 1632. The university still is the heart and soul of the town giving it a youthful look. There sure is lots of young people in Tallinn, too, but in Tartu you really can see and feel that you are visiting a town with many academic students.
Last time I visited Tartu was at the end of April. Here are some pictures I took during my visit. The university also has its botanical garden (founded in 1803) right in the town centre. In April only few flowers were blooming but I'm pretty sure it's going to be gorgeous in the summer.
If you ever come to Estonia I recommend you to visit Tartu in addition to Tallinn. By car, it's only 2,5 hours from the capital.