Mayan Palace is located in Orland Park, United States on 8600 W 159th St. Mayan Palace is rated 4.2 out of 5 in the category family restaurant in United States. yan Palace is a Mexican restaurant in Chicago. The inside dining room is a cozy environment for lunch or dinner, while the outside patio is a relaxing place to unwind with a delicious meal and a margarita. Both dining areas show off the classic Mayan style with dark, rich colors and themed decor. A short bar area stands on one side of the interior dining room, serving mojitos, margaritas, beer and some international wines.ood is offered at Mayan Palace for lunch, dinner and a late night snack each night up until 11 p.m. on weekdays and midnight on weekend nights. On Tuesdays and Thursdays, margarita pitchers are half price, making it an ideal place for a night out. Popular entrées on the lunch and dinner menu include the carne asada, fish tacos and the veggie enchiladas.