Hey Chahit, Search for the Zostels or hostels at www.hostelworld.com for a cheap and nice accommodation. You can ask the Hostel owner for the bike on rent. Happy travelling!!!!!
There are lots of rental bike agency in Pune from where you can rent a bike for a day or two maybe you can rent a bike for a month. Some of the prominent bike rental in Pune which either I or my friends have used I have mentioned here. Secondly, you can easily get these bikes on weekdays but for the weekend you need to book in advance. Sai Motor
Contact Number: 020–39937276, 8796528144 Snapbikes
Contact Number: 02069333696 Vroom bikes
Contact Number: 9766656637
Good luck!!!