Greektown's easy to access as a visitor to Chicago; it's just west of the Kennedy expressway, is not far away from the Loop (downtown), and is the gateway to the West Loop, full of hip bars and restaurants. Easy public transit access via bus or CTA blue line stops.
Perhaps some of the character of Greektown has been reduced in recent years. This is due to some of the classic Greek restaurants along Halsted St. closing, due to either families deciding to get out of the business or shifting business conditions; the closure of some of the Greek-focused retail; and the gentrification of the surrounding neighborhood, now one of Chicago's most affluent. That said, it still has a Greek feel: there's the Hellenic museum; cool, Greek-focused architectural details; Greek street art; and a number of excellent Greek restaurants at which you can still get an authentic Greek meal and Greek hospitality.
Worth a visit!