I am looking for recommendations for inexpensive, authentic "non-American" food in NYC - between mid-town and Chinatown - on Sunday evening?

If Taim is open near NYU for Falafel.

How about Carmine's in Times Square, 44th and Broadway? Fun, great bar, good family style Italian food.

Jaiya Thai on 3rd & 27th.. Its by far the best thai food I've had & I've been frequenting the place for 15 + years!

I recommend Korean BBQ in Little Korea, specifically Kang Suh located on 32nd Street near Broadway. Great food & prices. You may be able to snag a private room which is fun with a group.

Chinatown can be kind of a dead zone at night, especially on a Sunday. But try Joe's Shanghai for soup dumplings or Great NY Noodle Town for duck and noodles and more "authentic" than not. Both are cheap and tasty. Better to get dim sum if you're going for brunch/lunch since that's when it's meant to be eaten; I like Jing Fong on Elizabeth or Dim Sum Go Go which is a little less traditional but might feel more manageable.

There's also a Xi'an Famous foods on East Broadway, though there aren't any seats. A new location opened up on St. Mark's that does have a stools, but seating six at once might be tricky. It's not mainstream Chinese, so maybe take a look at the menu.

In Koreatown, there are a couple of fun Korean fried chicken places: Bon Chon has an almost club-like atmosphere and is really loud, so might be fun for a group of teens, and nearby is KyoChon. I wouldn't say that either of them has particularly awesome food, but it's a fun experience. Kang Suh is good for sit-down Korean barbecue, but I don't know that it's the best or most favored place in the area; I've eaten there a few times, and it's always been good. In the East Village I like Dok Suni for Korean.

Have fun!

Thanks for the suggestions, they sound great. I feel like planning an eating/walking tour of Manhattan...

If you are fond of Malaysian cuisine , then I would recommend trying out lautnyc.com , its on 17th street. we had been there friday evening for dinner and it was fantastic.
Secondly, tomorrow its the final day of Malaysian Restaurant Week Celebration - so you can check out some other places too. Here's the link of participating restaurants - http://www.malaysiakitchennyc.com/news-events/events/malaysia-restaurant-week-2012. oh I so wished I could join you guys tomorrow afternoon. Have fun..

Not Asian, but definitely not American and would be perfect for teenagers: Caracas Arepa Bar (7th St. just east of 1st Ave.) Tiny, colorful, young and fun. Maybe a dozen types of arepas - with meat, seafood or veggie toppings, plus great sides - fried platanos with cheese, guacamole, various salads....they also have delicious coconut and banana shakes - nonalcoholic, so good for teens (beer/wine too.) Cheap. Very popular, so I'd call ahead with a party that big. In E. Village - fun area for kids too, as is Chinatown....midtown, not so much.

http://www.caracasarepabar.com/index_2.php