The first area you will normally be recommended to shop in is Ermou street, the pedestrian street that runs off Syntagma at McDonald's. Yes there are some good shops here for clothes, but veer off into the side streets for cloth and varied items and also try Monastiraki.
If you like big shops or to buy brands, head a for the Attica Center(Syntagma square).
The Attica department store will reward you with good views from its roof top cafe .
Some department stores are open everyday from 8.30 to 20.30 without a break. Tourist and other shops in tourist areas may be open for more hours and on Sundays.