you can find very decent (breakfast incl.) for around 60$ look at (
Online Hotel Booking for Cheap, Budget & Luxury Hotels in India | MakeMyTrip.com)
Plz dont stay at cheap and eat a cheap places.
u can rent car for 20$ all day/ plus gas. (mind you half of the time u'll be sitting in traffic)
metro works well too and so does auto taxis.
i suggest stay travel outside cities (of course once u see the major attractions), southern part of India is amazing/ goa/Andaman islands. kerela etc.
and dont go in winter. (cause of pollution during winter time)
get a sim, maybe ull need someone from india to sponsor u for a sim (security shit). but so cheap and unlimited internet for $10