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 amazing Kernave Archaeological Site, where you can see remains of the medieval town. For instance, if you like the newest 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). That museum is dedicated to the history under the Soviet rule as well as to repression against Lithuanian people.
In case to visit the second country, that is a paradise for history fans, you can take one of many cheap flights to Russia. When you are there, you will have a chance to visit places and sites where many crucial historical events took place (http://www.lot.com/airline-tickets/flights-to-russia). E.g., if you visit St Petersburg, you can visit the Church of the Saviour on Blood, that was built on the spot where Tsar Alexander II was assassinated in 1881.