Get tickets to see a game at Stade Josy Barthel. If there's nothing scheduled while you're there, you might like to check if they give a tour of the facilities.
You'll soon see why this Luxembourg City sporting facility is visited by many travelers. If you're searching for other things to keep you busy, Notre-Dame Cathedral, Grand Ducal Palace, and National Museum of History and Art are in the area as well. They won't take you very long to get to from Stade Josy Barthel.