Exarcheia is the most unique neighborhood in Athens, by far. It's not for everyone. It's gritty, graffiti-laden, and crawling with punk rock kids who are far more harmless than they appear.
But behind its rough exterior you'll find a dozen bookshops, tiny cafes where old men sit sipping Greek coffee, and an onslaught of art exhibits with political undertones. The neighborhood's cultural identity is diverse: you can smoke hookah with Syrians or you can dine with the artsy Greeks. Embrace every second of it.