Archaeological Museum, which is placed in eastern Lithuania. It is enough to mentioned that this outstanding museums is listed n the UNESCO list! There is also wonderful Kernave Archaeological Site, where you can see remains of the medieval town. E.g., 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 history under the Soviet rule as well as to repression against Lithuanian people.
To visit the second country, that is a paradise for history fans, you can take one of many cheap flights to Russia. Once you are there, you would have a chance to discover places and sites where the most important historical events took place (click here to visit this page). E.g., if you visit St Petersburg, you can visit the Church of the Saviour on Blood, that was built on the destination where Tsar Alexander II was killed in 1881.