My first trip to India cost almost nothing.
Round-trip ticket from Seoul was payed with my mileage for Korean Air and I had US$260 only and it was more than enough for almost two weeks of different journey spanning Mumbai, Chennai, Pondicherry and Auroville..
For the lodging in Collaba Mumbai I chose dormitory run by Salvation Army actually for back packers. It wasn't bad at all and quite fit for small spending and the humble space made me feel very young since I've never tried that kind of budget lodging after I graduated school almost 25 years ago.
Full moon in Bombay welcomed me at the very first night in the mysterious & different country.. :p