Buy a ticket and join the fans at a game at Tennis Point Vienna. If there's nothing scheduled while you're there, you might like to check if the stadium offers a guided tour of the grounds.
You'll have no end of sightseeing choices when in Landstraße. Tennis Point Vienna is a great place to kick off here, but there are plenty of other interesting sights to check out. Schönbrunn Palace, Vienna State Opera, and Hofburg Imperial Palace are near the sporting facility and and will cap off your day nicely.