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 modern history, you should definitely visit the Paneriai Memorial. That museum is dedicated to all victims of the Holocaust. Furthermore, there is also the KGB museum (also called the Museum of Genocide Victims). That museum is dedicated to the period under the Soviet rule as well as to repression against Lithuanian citizens.
In case to visit the second country, which is a paradise for history fans, you should take one of lots of cheap flights to Russia. Once you are there, you would have a chance to discover places and sites where the most most important historical events took place (see what i found). For instance, if you visit St Petersburg, you can visit the Church of the Saviour on Blood, that was built on the location where Tsar Alexander II was killed in 1881.