Buy tickets to see a game at Tbilisi Sports Palace. If there's nothing scheduled while you're in town, you might like to check if the stadium offers a tour of the grounds.
This sporting facility is often on the itineraries of travelers to Saburtalo. But Tbilisi Sports Palace isn't the area's only highlight. St. George Statue, Narikala Fortress, and Metekhi Church are some other worthwhile sights nearby.