In my opinion the best way to experience any culture is through its food. Not to mention I find syrian dishes healthy as well.
I love Kibbeh b'Labaniyeh. Are kibbeh balls slowly cooked in a creamy yogurt sauce, with a saute of minced garlic; the garnish: fragrant flecks of dried mint and a sprinkle of spicy paprika. It tastes really good.
But to be honest, I like everything i've tried. Fattoush (vegetables sald with bread) or the traditional meat pizzas called lahm bil ajin. Even better is the fact there are small bakeries where you can prepare your own meat mixture, and the bakery will make dough and form all the pizzas for you.