Iron Curtain, HKV, a few months ago, when friends who do this sort of thing more than I do and are forever an inspiration, asked if I wanted to go along and watch Woody Allen's Manhattan. Lovely comfy seats, AC at just the right temperature and armrests wide enough to balance your drink--because yes, you can drink inside. I took the Good Thing again on his birthday, we watched an Argentine movie, and each time I go, I wonder why I don't more often. (Then I remember, "Oh yes, there's Hauz Khas Village outside.") The hitch is that their DVD or whatever they're using often skips, leading to a lot of "TCHAH" noises from the audience. But! Free!
* All the Centres--by which I mean foreign cultural centres. But you already know this. The two best are the American Centre (sticky about security, leave everything in your car, but then, the parking situation is a bit bad, so maybe just carry your wallet + ID) and the Japan Foundation Cinema Club (where I've never been, but gosh, doesn't it look lovely? All those animated movies!)
* The Habitat Film Club often has some obscure and lovely Indian movies. Okay, this is not FREE-free, but for Rs 938 a YEAR, you get to watch movies all the time, and join workshops and things if workshops are your thing. (I personally am a bit fidgety so not an ideal workshop participant.)
* There's a place in Gurgaon called Epicentre that screens some nice movies. I don't know anything about it because I don't go to Gurgaon.
* Cine Darbaar organises a lot of the American Centre screenings, but you should keep an eye on them, because they regularly do fun shit. A Japanese animated movie festival, for example.
* Just stumbled across Enlighten in my various internet wanderings. It looks cool and spiffy, the website is slightly confusing in that hipster, intimidating way, but it looks like most events are in Bombay. Bombay! You're so cool! I miss you!