The main shopping street, Ermou, is at the center of Athens and is for pedestrians only, so you can go window shopping unobstructed by car traffic. In Kolonaki and Glyfada you will also find many well known brand names and haute couture boutiques to choose from.
For souvenirs and small objects Plaka and Monastiraki are the ideal spots. The neighboring Athenas Street has many herb and spices stores and a bit further down the Varvakeios market place is a sight worth seeing, even if you do not wish to buy any meet or fish.