When you visit Athens you're going to find street vendors all over the place. From the tourist streets of the Plaka to the street corners in the every day neighbourhoods, there's always someone willing to sell you something. You can really boil these vendors into 3 groups; people selling fake high-end merchandise, people selling legitimate products, and people selling food.
The people selling knock off merchandise are probably the most prolific. You can find them everywhere either selling their wears or running from the authorities. Two things to keep note, it is illegal to do business with these vendors and the items they sell are poor quality.
The people selling legitimate items tend to congregate in groups, the biggest and best of these groups can often be found around Thissio Metro station, particularly on a warm summers night. My favourite of these vendors are the folks selling hand made crafts, art, and jewellery. The quality of the hand made items depends on the craftsmen, however you'll likely walk away with something unique and original. Around this area you may also find a few vendors selling Greek antiques, some less antique than others. Many vendors sell antique Drachma, which makes for a pretty interesting souvenir.
The street food in Athens is average at best. Stopping at a place like Monastiraki for a Koulóuria (bread ring) or some fruit from the local vendors is fine, but if you want a meal you're better off stopping at a taverna or gyros shop.