The Greektown Casino is my favorite Detroit casino. First, it's located within walking distance of everything downtown and parking is easy in their massive garage (on a non-baseball game day). The Motorcity and MGM casinos are located away from downtown and not in walking distance which is a pain if you are coming from a baseball game or dinner.
Greektown probably has the most slot machines and is usually the busiest. Therefore, also the best for people watching.
Nestled away on the second floor, you can find the penny slots which are almost impossible to find at the other casinos.