I had good luck buying an Aircel SIM at Big Bazaar in the Ambiance Mall yesterday.

I know that I overpaid for the SIM (it's labeled Rs. 49 and I was charged Rs. 250+90 and then sold an Rs. 500 refill), but I managed to walk in with nothing but my passport and a locked iPhone and have my photos taken, phone unlocked and everything taken care of in about ten minutes. I've bought SIMs in the states and had a harder time.

They were perfectly happy with my hotel address and multiple-entry business visa. They photocopied everything and had me sign each of the copies (and across the photo). Even had a nice chat with the guy about the new unlocking method for the iPhone that only requires browsing a website.