Buy a ticket to watch a game at Biomedical Campus Rome. If there's nothing scheduled while you're in town, you might like to check if they give a tour of the grounds.
You'll find Biomedical Campus Rome in the farming township of Zona XXVI Castel di Decima. Entry here is free, so you can leave your cash zipped up in your daypack. While you're in these parts, why not tick off a few other great sights, such as Museum of Roman Civilization, Cinecitta World and PalaLottomatica?