Right off of Vabaduse Valjak (Freedom Square) is the Niguliste Church, one of the Old City's more recognizable sights. My first time there was in preparation for the September 11 10th anniversary concert.
Niguliste is no longer a church, but it used to be. It was finished in 1230...inside is this amazing tapestry that is nearly as old. The church was particially destroyed by the Soviets in the bombing of Tallinn.