Like all good non-sedentary cultures, Saudi Arabia borrows extensively from its more sedentary neighbors to provide lots of great food choices (thank you, Yemen). Levantine pies are easy to find here, from fast food chains to much more authentic places.
Or you can make them at home. I use Paula Wolfert's dough from The Cooking of the Eastern Mediterranean, except that I use whole wheat flour. There's enough olive oil in the recipe that the dough is still tender and delicious. There are so many recipes out there for the dough.
Preheat a baking stone to at least 450 degrees for at least 30 minutes. After it's hot, pinch off a bit of dough (around 60-70 grams) and roll it into a very thin oval. In my opinion, the most important part of making fatayer making sure the dough is thin. Let it rest for a minute, then put the filling in a wide strip in the middle of the oval (the long way). Fold the edges of the dough over the filling but don't cover the filling, then pinch the ends to make a boat shape. It might take some practice but even if it looks weird, it'll taste good. Bake on the hot stone till its golden on the bottom - it'll depend on how hot your oven is.
There are so many fillings you can use. One easy one is to sauté a bit of onion and garlic in olive oil, then add some chopped greens and quickly cook them down. Drain and press out as much liquid as possible before using as a filling, and add a squeeze of lemon and some salt to taste too. You can sprinkle on some feta if you want.
Cheese with tomato. Cheese (experiment with Middle Eastern cheeses, and soak them first if they're too salty, or just use the kind of feta you get in US grocery stores). Cheese with zaatar. Labnah with a drizzle of honey after it's cooked. Labnah with zaatar. Cheese with mint. Cheese with mint and tomato. Chicken and mint. Potato and mint. Potato and cheese. You get the idea.