If you are interested in non-desi food in Chennai, check out Cedar’s in Kotturpuram (I don’t know the exact location, if I am not mistaken its not far from Gandhi Mandapam) which serves Lebanese food.
The food is excellent. The restaurant feels more like a house with an upstairs, terrace etc., so you don’t feel like you are eating at a restaurant, which is nice. There was nice middle eastern music playing all along.
To add to this, when asked, the cook and the waiters (all Indians trained under a Lebanese cook who worked here for 2+ years) are capable of "radiating lots of fundas" about the food and the cooking, like you normally observe in western countries. The costs average about Rs. 300+ per dish. Sheesha (hookah) is also available at the restaurant.
The picture shows the cook (Sundar) and the waiter (Milton), both were very impressive with their knowledge of Lebanese food.