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 wonderful Kernave Archaeological Site, where you can see remains of the medieval town. For instance, if you like the modern history, you should absolutely visit the Paneriai Memorial. This museum is dedicated to all victims of the Holocaust. Furthermore, 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.
To visit the second country, that is a paradise for history lovers, 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 (more here). For instance, if you visit St Petersburg, you could visit the Church of the Saviour on Blood, which was built on the location where Tsar Alexander II was killed in 1881.