For someone that loves history, Athens is the place to investigate the beginnings on which our modern society is based. Here are a few "must-visit" places:
Acropolis: goes without saying
Acropolis Museum: this museum is modern and innovative. It has a wide range of artefacts from the acropolis and surrounds and the best part is that there are archaeologists on the floor so you have direct access to people that really know their stuff.
Agora (both Greek and Roman): This was the hub of Athenian society.
Pnyx: the birthplace of democracy.
Socrates prison: you can see where the dude resided. This is on Philopapou hill where Pnyx is so you can just do a tour to check them both out.
National Archaeological Museum: artefacts from 4,000 BCE onwards. Even has Egyptian artefacts.
Benaki Museum: has more recent history from Byzantine to more modern history.
Just walk around Athens and you will come across archaeological sites that are right in the middle of the street. For example, the Pnyx and Socrates prison aren't behind a fence that you have to pay to get in. Others are Hadrian's Arch, Monument of Lysicrates, the Roman Baths on Leoforos Vasilisis Amalias and so much more!
Enjoy your trip!