Here I am replying to my own post
It's almost hard to pick a favorite, since I'd choose something for nightlife, something else for a cafe, something else for sightseeing, etc.
But in my opinion Monastiraki is so interesting - I think you can buy anything from a foustanella to a frying pan! The Sunday Athens flea market is there (Sunday's the only time it's a true 'flea market'), and there's the Central Meat & Fish Market (north of Athinas) . Morning is the time to go and you don't have to be buying 'groceries' to enjoy the experience, with its butchers hall, fish stalls, sausage sellers, etc. And at night, there is an authentic Rembetika Club above the Meat Market of all places! Now where else in the world would you find that??