Step 1: Understanding the passage.
The passage explains that sports were an important part of ancient Greek culture. It mentions that the Greeks were pioneers in organising sports systematically and hosting competitions in various events like discus throw, wrestling, and chariot races.
Step 2: Finding the answer.
The passage clearly states that the ancient Olympic competitions used to be held at Olympia, an ancient Greek city.
Step 3: Conclusion.
Hence, the city where the ancient Olympic competitions were held is Olympia.