I just learned that they are now open on Saturday's. YEAH! My Mom and I stopped there for lunch today (Saturday), and it was empty. As we ate, a few more people stopped in. I don't think everyone knows they are open on Saturday's yet, but hopefully the business will pick up.
I discovered this place thanks to some friends at work. Since my first visit, I've never been disappointed. I always order the Chicken Picado Pita and it is always so delicious! Just the right chicken to pepper and onion ratio. The pitas are fresh, the tzatziki sauce superb and their french fries are magnificent -- crispy outside and melt-in-your-mouth buttery inside. Although I've yet to venture outside my own menu choices, they have plenty of items to choose from and I'm sure just as delicious.
The staff is friendly and accommodating. The parking is limited if you get there on a busy day, but otherwise it isn't too hard to find a spot. Like others have mentioned, it is right on the light-rail route so the location is great too. They even have a small patio out front where you can enjoy your food and the Phoenix weather (when permitting).
If you are out and about in the downtown area during the week or Saturday, definitely give Athenian Express a try. It is one of those affordable, quality food gems that you shouldn't miss out on.