Zaytune Mediterranean Grill is located in Chicago, United States on 3129 S Morgan St. Zaytune Mediterranean Grill is rated 4.4 out of 5 in the category mediterranean restaurant in United States. tune Mediterranean Grill is a restaurant that is located in the sun-filled city of San Antonio and is situated just off a major roadway, making it easily accessible for residents and tourists alike. This spacious venue offers a casual and laid-back atmosphere and is a favorite for families and private parties of all sizes. The interior of Zaytune Mediterranean Grill is styled with large windows, colorful walls, recessed lighting and is full of character.sts of Zaytune Mediterranean Grill are invited to choose from a lengthy menu of authentic Meditation cuisine. Menu items include roasted eggplant dip, falafel platter, chicken kabobs, watermelon cake, saffron rice and gyro wraps.