Food - it's edible culture

I like food. My parents are very capable cooks, with an interest in food from all over the world, and trying new things, all traits they have passed on to me.

New York is a cosmopolitan town, with as many as 800 languages spoken there according to Wikipedia. I'm hoping that means there are foods available from almost as many cultures. And I wanna try them all (or at least some of them.)

I'm not really interested in trying the archetypal New York foods: I've eaten pizza and hot dogs and cheesecake before. I'm not in to sweet things, so waffles and doughnuts and the like have no appeal. And I don't want to waste my eating budget on things that I have or can eat here: Mediterranean (Greek, Italian, Spanish), European (French, German), Asian (all of them), and the Indian sub-continent.

I do want to try things I can't get here. Like kosher food, including bagels (and how is lox different to the smoked salmon we get here?), and pastrami on rye. And Central, Latin and South American food (the Mexican food we get here is very ordinary in my experience).  And Soul Food (which I presume is from the South). And West African (a Jamaican friend put me onto jerk chicken long ago). And, and, and.

Wikipedia associates the following Manhattan neighbourhoods with these cuisines:

• Lower East Side - Puerto Rican, Kosher and Latin American
• Harlem - African-American, Latin American, West Indian, and West African
• Washington Heights - Dominican, Puerto Rican and Jewish
• East Harlem - Puerto Rican, Mexican, Dominican, and Italian along Pleasant Ave
• Little Italy - Italian [not so much these days] and Chinese
• Chinatown - Chinese and Vietnamese
• Koreatown - Korean
• East Village - Japanese, Korean, Indian and Ukrainian
• Murray Hill - Indian, Pakistani and Bangladeshi
• Upper East Side - German, Czech, and Hungarian

So that's a starting point. Got any places you particularly recommend?