Plaka is the oldest residential district of Athens. Its historic narrow lanes and stepped alleys wind up the lower slope of the Acropolis. Once the heart of working class Athens, then the centre of music and nightclubbing, nowadays it's full of cafes and restaurants, also shops which tend to be aimed at tourists with prices to match. But it's definitely the nicest part of Athens to wander around between visits to the nearby archaeological sites and museums.
Head up the steps to the small area of Anafiotica. This is like a little Greek island village transplanted to Athens. It was built by the migrant workers who came to build the Presidential Palace in the 19th century when it was King Otto's palace.