Disclaimer: I am not Greek. Not even a hair. But I love Greek food.
When I was in college there was this diner that I would go to at 4 am to study. The overnight waitress was always crocheting. She knew me on sight by the time I graduated. Anyway.
I would always get a grilled cheese, fries, and a pickle. To start I'd have a diet coke, and after eating I'd get a coffee. All of this is trivial, except she new what I would have maybe the third time I was there. She would patiently get me more coffee and not bother me about taking a table up- granted- it was not busy but I was taking up some space.
There are a TON of dining options in Greektown. 24 hour diners to fantastic food. I have eaten at 9 Muses- which is one of my favorites, the Parthenon, and The Greek Isles, among many others. I have yet to find a bad thing to say about any of the places I ate.
Given its proximity to my college UIC and where I lived at the time it is no wonder I was there so much. I also learned a great deal about the culture and learned to appreciate it mostly by watching... but some questions- which were always patiently answered.