Hmm .. that journey is surely more than just a weekend trip ?
There are direct flights, trains and buses for this journey. Travelling by train is the cheapest way of getting there. Chennai (Tamil Nadu) to Pune (Maharashtra) distance is 1190 km and you can get there by train in just over 19 hours and 35 minutes. However, flight tickets come also cheap with fares starting from ₹ 2591.
The weather is amazing right now. You'll have a great time.