Get tickets and join the crowds at a game at Arena Manawatu. If there's nothing scheduled while you're in town, you might like to check if they offer a tour of the grounds.
You'll have no end of sightseeing choices when in Palmerston North. Arena Manawatu is a great place to start here, but there are many other worthy places to appreciate. The Square, New Zealand Rugby Museum, and Victoria Esplanade are close to the sporting facility and will top off your day nicely.