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 newest history, you should absolutely visit the Paneriai Memorial. That museum is dedicated to all 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 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 should take one of plenty of cheap flights to Russia. When you are there, you will have a chance to discover 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 destination where Tsar Alexander II was assassinated in 1881.