Greek food has been available there for many years
A reasonable restaurant where you can get authentic Greek food is Greek Souvlaki. The gyro may be the most popular item on the menu, but they have a wide variety of foods from which to choose.
Greek Souvlaki was started in 1972 by Lee and Mary Paulos. They tried to provide great customer service and good quality products. The couple retired in 2000 with their sons taking over the business. They have now grown to four restaurants.
Souvlaki, is a popular Greek fast food consisting of small pieces of meat and sometimes vegetables grilled on a skewer. It is usually eaten straight off the skewer while still hot. It can be served with or inside of a rolled pita, typically with lemon, sauces, vegetables such as sliced tomato and onion, and fried potatoes as a side. Wikipedia
The menu items at Greek Souvlaki include a wide variety of Pita Sandwiches and Gyros with various meats, cheese, or vegetables.
They offer a choice of white (Tzatziki) or red sauce with their food. The white sauce is a creamy combination of yogurt, sour cream, cucumber, and garlic. The red sauce is a Greek marinated tomato base with ground beef and a spicy kick.
There are also a variety of Souvlaki. They have rice bowl dishes which include lemon rice, garbanzo beans, cucumbers, red onions, and tomatoes with a choice of meat. They have spaghetti and soups. There are also salad options including the popular Greek salads. There are some specialty items on the menu as well as dips and pita.
They do take out orders and have catering as well as dine in options.
Besides the Salt Lake City location at 404 East 300 South, there are Greek Souvlaki restaurants located in Murray, South Jordan, and West Valley. They open at 11:00 AM and close at 9:00 or 10:00 PM. They are closed on Sundays.