Along with what @Sgee has provided, which is great advice, I would add Central Asian and Caucasus foods. While LA does have Georgian, it is generally an offshoot of Armenian restaurants. In NY you will find full menus full of so many dishes, not just khachapuri and khinkali. There are also a lot of good Uzbek and Tajik restaurants. Most of these are in Brooklyn, although Queens has some Kosher versions in Rego Park.
Explore Caribbean as much as possible, that is what is missed most about NYC. Southern Caribbean cuisine from Guyana and Trinidad and Tobago flourishes in the Ozone Park and Richmond Hill areas. Over 15 nations from the Caribbean at least are represented. Haitian food in Brooklyn is to die for.
If you go to Jackson Heights as suggested, eat at the Bangladeshi places. Indian is not as interesting there as it used to be, and as noted places like Edison (and Oak Tree Road is magic) in New Jersey are much better. Not sure what the status at the Ganesh Temple canteen is right now, but for excellent southern Indian in Queens that is a good stop.
Also in Queens, in the neighborhood of Astoria, is a few blocks of Steinway Street often called “Little Egypt” but this undersells it, as there is also Moroccan, Algerian, and food from throughout the Levant. More great Middle Eastern food and wonderful community is in Bay Ridge, Brooklyn.
Do get some Puerto Rican as suggested by @Sgee as well, and the Bronx is the best place for that. 188 Cuchifritos is always a trip.
What am I missing?? 