If you want to see a show while you're in town, try and grab some tickets at E-square in Shivajinagar. If you want to experience more of the culture Pune has to offer, head to Fergusson College, Sinhagad Fort, and Shaniwar Wada.
If museums are on your list of things to see, you might want to browse the collections at Mahatma Phule Museum in Shivajinagar. If you want to see more of the museums in Pune, Raja Dinkar Kelkar Museum isn't far either.