Gifts and souvenirs in Athens should be bought at ‘Monastiraki’ Flea Market. It is difficult to define this market as flea market except on Sundays, when some of the shops are closed and vendors bring a variety of tables and carpets to sell “fleas” and antiques.
During the rest of the week, the market has more of a bazaar feel. Most stores are designed to suit fairly conventional tourists.
On Sundays, you can find, among other vintage items, paintings and jewelry. You should walk to the ‘Psiri’ street nearby to visit some of the art galleries and vintage shops.