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 definitely visit the Paneriai Memorial. That museum is dedicated to the victims of the Holocaust. What is more, there is also the KGB museum (also called the Museum of Genocide Victims). This 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 fans, you should take one of tons of cheap flights to Russia. Once you are there, you will have a chance to visit places and sites where many important historical events took place (see what i found). For instance, if you visit St Petersburg, you could visit the Church of the Saviour on Blood, which was built on the spot where Tsar Alexander II was assassinated in 1881.