Byron was a figure directly related to Greece and Greek ideas, that is why you can find his statue in Athens, next to the National Garden and Zappeion. Lord Byron’s life was during the Greek War of Independence, which supported both financially and ethically. Psirri area is also related to Lord Byron, who lived there.
The places that are related to Lord Byron today and you can visit, is the Lysicrates monument, where the Cappuccini monastery that Byron lived was, but also the National History Museum (Stadiou 13 str. or the old Parliament of Athens), where you can see Byron’s personal belongings.
Byron’s personal relation to Greece is also during the two first loans that guaranteed the new born state’s existence. Byron acted with his reputation in order to convince the British audience to “invest” to Greek Independence Rally against the Ottomans, in a period where the official UK policy was not supporting the Greek cause. Moreover, a municipality at Ymmitos mountain brings his name in honor.
Here is a list for more Athens museums.