The Plaka is the name given to the tangle of narrow streets and pedestrian ways between the acropolis and Syntagma square.
The Plaka is a tourist area, and like tourist areas anywhere in the world there is more than enough souvenir shops. T-shirts, calendars, postcards and dolls are available at almost every second store. This is Athens though and there are also any number of stores offering cheap reproduction of greek art, statues and pottery. Between the tourist shops though there are a few gems offering more substanbtial fair, including a number of original galleries, shops selling Flokati rugs and craft and antique stores. It is possible to wander and browse at your own pace too, without being accosted by tourist touts.
In the evenings, starting at around 7.00pm, the Plaka starts to come alive as a restaurant area, with the taverna's and cafe's all offering al-fresco dining. There can be few better ways to spend a summer evening than people watching from a table in the plaka. Greek wine is cheap and most of the tavernas offer an extensive and inexpensive array of dishes. You would have to be pretty hungry to not get change from 15 euro per person (including wine). It is similar food wherever you eat though so feel free to choose for location.
Children are adored too, so parents needn't feel self conscious.