The changing of the guard ceremony, performed by the Presidential Guard, is conducted in front of the Tomb of the Unknown Soldier on the area between the Syntagma Square and Parliament building.
This happens every hour, on the hour, 24 hours a day, 356 days a year. There is a bigger, ceremonial parade at 11 am on Sundays. It is a no miss activity, so schedule your day including the changing of the guard ceremony but have a bottle of water with you and a hat in case you watch it during day times with high temperatures.
To reach Syntagma Square, just take the metro Line 2 from Metaxourgio station towards Elliniko - for just 3 stops and get off in Syntagma Station. Alternatively take a taxi from the hotel to reach the area in 10’.
Hop On Hop off bus pass through Syntagma Square as well. Indeed a very fun way to explore the city.