There are several good Greek fast food chains like Goodies, Everest, Grigories and Black Sheep that sell sandwiches and I recommend them. Goodies also sells hot food like burgers and fries too. The Greeks distinguish this type of hand food into two main categories: Salty and Sweet or almyra and glyka. These chain stores all have unique signage and bright lights and are not a traditional type of Greek place to eat. Still they have their place and are far more interesting than McD's or BK.
I also recommend the more historic and smaller little no-name independent pie shops and bakeries which sell traditional Greek fast food like pies "sto hyeri" (in the hand) with fillings including ham, chicken, cheese, minced meat, spinach, mushroom. You'll notice stores like these all over Greece and the hole in the wall places can be better than the bigger establishments too, especially if they are Mom and Pop operations which have been in business for years. Many bakeries also sell these same traditional pie items in addition to loaves of bread. So in general no matter what kind of place you find yourself in, if there are Greeks in there buying stuff, than you can bet its decent. Don't be afraid to experiment. Read some more and you'll have a good idea what is going on.
As mentioned, besides a ham and cheese pita you could choose a sweet pie too. Worthy of eating are the traditional, and only in Greece, bou-ghat-ses. Boughatses have sweet cream fillings and are like a pastry but sprinkled with powdered sugar and cinnamon. They are usually rectangular in shape but its up to the individual baker.
Triangular walnut sweet pies are another must try type of Greek fast food and are called kareedo pites. Almond pies are ordered by saying amigdalo pita which I also highly recommend trying. Imaginative bakers may come up with other delicious combinations so it pays to ask if its not too busy.
Since the invention of electricity, the modern Greeks have liked to toast their sandwiches in special toasting devices, which remind me of a waffle iron. I don't know why they do it this way, they just do and its a bit different. Greeks call toasts like this oddly enough toasts.
You cant really call these 'toasts' part of traditional Greek cuisine can you? Try one and let me know. Its more of a 'Mediterranean thing' likely. Anyway, one day, after spending a lot of money on shop bought toasts, I went out and bought a toaster grill for 70 eu and it changed my life! These grills are pretty handy things to have around but hard to clean if you tend to melt the cheese as I do. Pictured left is a professional version and I may have to upgrade soon. I am on my second toaster grill and currently using a 'bosche' model. Its as hard to clean as the generic version I wore out. German engineers aren't quite as efficient as they are made out to be in this case. Guys have you ever used a toaster grill? Well please give it a go.
Toasting is optional when you go into a sandwich shop and it takes longer too. Some of the chain stores mentioned above will have sandwiches pre-made and ready to be toasted. You know the kind of thing: ham and cheese, chicken and tomato, cucumber, cream cheese and olive and so on. They do that in Italy a lot too but in Italy they have special kind of toasting bread which they don't seem to do here in Greece.