Mount Hymettus (Imittos) offers many interesting biking routs with lots of dirt roads. It generally requires a good mountain bike with the right tires. Expect some steep biking climbs that are nonetheless negotiable if you have some biking experience. There are specialist maps that show designated routes that are good for biking.
Athens has also changed in recent years with many auto-free zones around the central area in particular. This includes the area from Gazi/Keiramikos to Thisseo and on to Dionysiou Argeopagitou street which takes from Thisseo to the Acropolis Museum. The green areas around there are also accessible by bike. Hermou street from Syntagma down to Thisseo is also pedestrianized, giving bikes access to the most important parts of Downtown Athens. Pedal through the Plaka and Monastiraki districts, as well as the old neighbourhood of Anafiotika, part of Plaka. The green Philoppapou hill and the Pnyx are a particular pleasure to bike through. This is where Socrates Cave lies, as well as the tomb of Kimon, leader of the Delian League. The area is also where Plato lectured.