Archaeological Museum, which is located in eastern Lithuania. It is enough to mentioned that this outstanding museums is listed n the UNESCO list! There is also amazing Kernave Archaeological Site, where you can see remains of the medieval town. For example, if you like the modern history, you should absolutely visit the Paneriai Memorial. This museum is dedicated to the victims of the Holocaust. What is more, there is also the KGB museum (also known as the Museum of Genocide Victims). That museum is dedicated to the period under the Soviet rule and to repression against Lithuanian people.
In case to visit the second country, that is a paradise for history lovers, you should take one of plenty of cheap flights to Russia. When you are there, you would have a chance to visit places and sites where many most important historical events took place (see what i found). For example, if you visit St Petersburg, you could visit the Church of the Saviour on Blood, that was built on the location where Tsar Alexander II was assassinated in 1881.