I love Shawarma! If you are scared of the carts in the street and their "side effects", I suggest you try Kosher Deluxe located midtown. Ok, this restaurant is serving a wide range of food: Middle Eastern, japanese, chinese...I have only tried the Shawarma and the falafel and they were delish! They serve it in different ways: pita, baguette or plate and you can pick Hummus and / or hot sauce. Each sandwich is coming with salad (there is a salad bar) also very good, for a little over $10.
So, what is Shawarma? It is a Middle Eastern sandwich with pieces of lamb, goat, chicken, turkey, or a halal mixture of meats that cooked on a spit for sometimes an entire day. The way the meat is cooked is very important: it has to be upright to give that wonderful taste. Some argue that Shawarma is different from a Gyro because a Gyro is a mixed of beef and lamb.
If you are adventurous, try the gyro in the cart situated at the corner of 6 avenue and 53rd street. It is well known and very good. But make sure you go to the South West corner cart, otherwise, if you go to the South East side cart, you will probably understand what I meant by "side effects".
Enjoy!