Check out the outskirts - the lakes Mulshi, Panshet, Khadakvasla, Pashan. The Sinhagad Fort, Lonavala and Khandala hill stations. There is Kaivalayadham nearby and Igatpuri's Vipassana centre. Go to nature Cure centre.
Apart from this, it has excellent restaurants, great theatre, classical music performances twice or three times a week. Plenty to do. Pune University is nice. So is the Bhandarkar Oriental Research Institute.
Quick Tips:
Stay on and sink into the place - give yourself six months and undertake to learn something of Indian culture. It is in many ways the best of the east and the west, so living and learning are both possible - it is the Oxford of the east and also the cultural capital of Maharashtra.
Best Way To Get Around:
Autos or rent a scooter.