Based on interest you can select either Jaipur or Pune.
If you are interested to know about the rajasthani culture and history you should go to Jaipur or if you are interested in natural weekend getaways you should choose Pune because Pune has some nearby weekend getaways full of nature .
That's a question! but it depends on your personality i.e A hill/mountainous person or love ancient architecture.
In outskirts of Pune you have so many places to visit like Lonavala, khandala, lavasa Imagica. and for summer/Rainy season the beauty is in its peak. You'll get peace here, from sunrise to sunset view is mesmerising. Imagica is fun, theme park is a all day fun activity. For Jaipur, it's a very beautiful place, one of the best architecture, hawa Mahal the trademark of Jaipur, then Rajasthani culture, then the fort. so both places are good at there respective point but you need to found in actual that which personality you are and after that you'll answer by own. I hope I made a point here! thanks
I think Jaipur is an amazing city which offers you lovely palaces. i remember, when I'd gone to Jaipur, it was the first time I'd actually visited a palace and since that very day, I fell in love with history.