UNIQUE FOOD OF NYC - Coming from Los Angeles
I wish A Salt And Battery had not given up on its' East Village location - you could have tried a deep fried Mars bar. Aside from this, and Surly's above-mentioned grasshopper treats, I might suggest the Cow Penis served up at Kenka's, on St. Marks, except for the fact that there are lots better dishes to try at far better eateries. If you've never tried Takoyaki (Octopus Balls), you might want to check out Otafuku, a street food stand on 9th street, not far from 2nd Avenue. Also, a number of places in Chinatown, including, if I'm not wrong, Congee Village, serve up Frog Casseroles.
Now, if we were talking outer boroughs, I might suggest Rego Park's Cheburechnaya for Ram's Testicles, or Flushing's A Fan Ti for that Goat's Eyeball fix.
taka, which is a japanese restaurant on grove st at seventh ave south in the west village, used to serve a great deep-fried grasshopper appetizer. i'm not sure if they still have it, though - the last time i was there (about 4-5 months ago) the waitress had no idea what i was talking about when i tried to order it.
I 2nd Keen's and Katz' Deli and Rocco's.
I would go for soup dumplings at Grand Sichuan, New Green Bo, or Joe's Shanghai. But skip dim sum, seafood, etc.
And there's always Momofuku Ssam Bar for terrine, sweetbreads, pork buns, banh mi. Not really unique food of NYC but David Chang is, IMHO, a genius.
I'm not sure if you guys have this in LA yet but there are a number of high-end dessert bars in NYC now. Kyotofu, Room 4 Dessert, Chikalicious. Or the dessert tastings at WD-50 or Varietal.
im a huge fan of Yakaniku JuJu for korean/japanese BBQ. its a little hidden away gem on 28th street between 3rd and lex. Not your typical korean in korea town, but its tiny (i think only about 15 seats) and on the second floor of a building. They have an "all you can eat" option which will basically give you a heart attack.
I think the following is unique to Manhattan (for an LA eater):
Great Bagels- go to Ess-A-Bagel...period
Jewish- go to Katz Deli and Diamond Dairy (noodles and cabbage!); get an egg cream in the East Village
Coal Pizza- go to Patsy's in Harlem and/or Arturo's
Middle Eastern- wait in line for meat and rice some evening at the famous 53rd and 6th Avenue street vendor; check this board for great falafel places
Greek-get a gyro at Gyro II across from Penn Station (really)
Red Sauce Italian-go to Ralphs on 9th Avenue; go to Lazzara's for great subs and pizza
Italian deli-get an Italian sub at Faicco's on Bleeker
Italian bakery- get great cannoli at Rocco's
Old School Steakhouse-Sparks
Eastern European-Valeska (also has familiar diner food)
Old bars-Chumley's (the unmarked door at 86 Barrow Street) or White Horse Tavern
Dont waste your time with:
...you've got great versions of these in LA
I agree on the bagels. Get as much as you can get.
For Jewish deli food, first go to Langer's in LA for pastrami so you can have a perspective when you try the ones in NYC. I happen to like the pastrami at Langers better than the ones in NYC, including Katz (so did Nora Ephron in her New Yorker piece a few years back).
I agree on the pizza. Go to some of the old-school NY institutions.
For Greek, you can get good gyro and souvlaki at Papa Christo's in LA, so I would focus on Greek seafood or the mid-high end places that are much better in NYC.
For steak, I think Peter Luger or Keens will give you a better NYC experience with the ambiance, but Sparks is no slouch either.
For eastern european, I think you should get to Greenpoint in Brooklyn.
Not sure the old-school italian isn't available in LA. Again, I'd rather focus on the higher end Italian if you want something more unique.
Skip Cuban in NYC, unless you go out to Corona Queens or to NJ. You can find better in Silver Lake, Atwater, or Venice.
Old bars are always classic.
Other reccomendations would be Egyptian in Astoria, Turkish at places like Ali Baba or Hemsin (in Sunnyside), Grand Central Oyster Bar for the classic NY feel,
Don't bother with Japanese ramen or Korean in NYC, there are much better places in LA.