The Plaka is a lovely pedestrian-only labyrinth of alleyways adorned with restaurants, jewelry stores, tourist shops, tavernas, and Byzantine churches. It connects with the ancient Agora and has been used for over 2,500 years as the shopping area and is a shoppers delight.
At one time, it was the nightclub district, but most of these establishments closed down when the government outlawed amplified music. today it is the favorite of locals and tourists alike for the charming cobble stoned alleyways of cafes, shops, tavernas and ancient ruins. Arguably the most fun neighborhood in central Athens.
Note: Gold jewelry in Greece is inexpensive, not because the price of gold is any cheaper but because labor is less costly. There are bargains for leather goods as well.
FYI: Most of the streets have been closed to automobile traffic, though you should still keep a watchful eye for a speeding motorcycle or delivery truck.