When exploring central Athens, there are several must-visit museums & monuments
that I would recommend. Here are a few notable ones:

The Acropolis of Athens 
Ancient Agora of Athens | 24 Andrianou st.
Acropolis Museum | 15 Dionysiou Areopagitou St. | theacropolismuseum.gr
National Gallery | 50 Vasileos Konstantinou St. | nationalgallery.gr
Basil & Elise Goulandris Foundation | 13 Eratosthenous St. | goulandris.gr
Benaki Museum | 1 Koumbari St. & Vas. Sofias Ave, Kolonaki & 138 Pireos St. | benaki.gr
Museum of Cycladic Art | 4 Neophytou Douka St., Kolonaki | cycladic.gr
National Archaeological Museum | 44 Patision St., Exarcheia | namuseum.gr
Museum of Kerameikos | 148 Ermou St.
Odeon of Herodes Atticus | Dionisiou Areopagitou St.