The New Gate is just another way into the Old City. There is a falafel place just inside to the left, but not worth stopping. The food is so-so and prices way too high. Eat at Jacob's Pizza instead
To ChofSep-you must turn left, after turn right and left- here is a greece orthodox patriarchate, go straight , after turn on the right and after the "papa andrey" shop turn left and turn left again.