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I can recommend Brick Lane on 6th Street:

http://www.bricklanecurryhouse.com/

I like Pongal as well. My favorite place though is Tiffin Wallah in Curry Hill. The restaurant is generally packed (but the wait is never more than a few minutes) and usually at least half the customers are Indian families, which I take as a good sign. Huge menu, prices are awesome, vegetarian.

Spicy Mina in Queens by the edge of Jackson Heights. It's across from a subway station... is very small... and technically the food is Bangladeshi but for most of us in the US that is a category of Indian food.

Don't be in a hurry as every item including appetizers is made to order at the time it is ordered. But it's worth the wait. This place is fantastic - I mean truly fan -frickin-tastic.

I would recommend Tiffin Wallah, in Murray Hill for a sampling of snack food/street food - it's really great and there's a fair amount of non-spicy stuff. There's a lot of fun items: if it's your first time trying Indian food, I'd recommend dosas, idli, the various kinds of chaat, and mango lassi (or if the place has it, falooda, a kind of custard/vermicelli dessert - I don't think that Tiffin Wallah has it though). I also like Sukhadia's for street-food style food (it's convenient if you're in midtown, as it's on 47th street and 5th). If you're up near Columbia, Indus Valley is good.
If you're in a group, it's good to order a rice dish (biryani), daal (lentil soup), some kind of vegetable curry and a meat dish (or two, depending on how carnivorous you are). Also, the breads (naan, a puffy flatbread) and puri (filled with various stuffings e.g. lamb, nuts and fruit) are really good.

If you can get to Jackson Heights though, I'd highly recommend - there's a huge South Asian community there, so there's a greater variety to chose from.

On a side note, if you want to try Sri Lankan food, there is a a place called Sigiri on 1st avenue and 6th street - it's different, but really good.