Because Greece has a relaxed approach to policing under-age drinkers it doesn't mean they will tolerate, a drunken free-for-all.
There’s no minimum age for consumption of alcohol, but you must be a surprisingly young 16 or over to purchase.
It hardly matters because it’s rarely enforced by bar and nightclub owners eager to separate young holidaymakers from their cash. No one asks for ID, not at the bar, nor the café not even at the supermarket (where you can buy just about any type of alcohol).
However drinking to excess is frowned on. You are expected to stay ‘nice’. Most Greeks do this by drinking moderately and eating mezze as they do. Try to follow the traditional Greek way, and drink moderately. Pick a taverna within walking (or short taxi ride) distance of where you’re staying.
Leave the quad bike at home. While not keen to enforce the drinking age, Greek police are keen to enforce drink-driving laws. The legal BAC limit is .05.
If you are sensibly making your way back to your accommodation on foot, take care on the winding roads; don’t fall off the edge and watch out for less responsible revellers (the ones on the quad bikes) coming around the bend in the dark.