आम लोग: "रेल फैनिंग आती नहीं". RailFans: "रेल फैनिंग जाती नहीं" - Md Asif

Visit Dagadusheth Temple which is famous Ganesh Temple in Pune and it's near to Pune Station. It opens from early morning.
If you are Tea lover, then take tea at Yevale Amruttulya which is beside of temple.
Then for breakfast try famous Puneri Misal Paav at Katakirrr or Sir Misal.
If time permits you can visit Shaniwarwada which is home of...
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Peshwa's. It's near to Temple only.

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First thing in the morning head to Appa near Gymkhana and try the awesome Sabudana Khichdi with Cucumber Raita known as Khichdi Kaakdi. You will thank me later. It opens at 7 am. There are other things to eat too. You can take an auto, uber, bus or can even walk since you have time.
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eaten, I would recommend strolling around in the old city area, also known as Peth area due to localities named after days of the week e.g. Shaniwarpeth.
It will be awesome early in the morning before it gets too hot.
Then you can visit Shaniwar Wada fort as suggested above. That should be enough for the time you have depending on how much walking and strolling you do.
If you still have 2 hours to kill, and money to spend, I would highly recommend taking an auto to German Bakery in Koregaon Park for an early lunch. It's an experience not to be missed.