To be frank, 'Quiet', 'Affordable' and 'Bangalore' are oxymorons to each other. Forget a combination of all three, you should consider yourself lucky to find a decent stay that offers any two of the three criteria mentioned by you.
The nearest place that can satisfy your requirement is 'Hotel Mayura Pine-Top' at Nandi Hills - which is a 1.5 hours drive (61 KM) from the heart of Bangalore city. 0815-6250906 - is the contact number for prior booking.
Regards,
Deb