If I want to send a letter to somebody on Roosevelt Island in New York City, what city should I send it to?

The ZIP code is 10044. Here is an interesting history of Roosevelt Island.

https://web.archive.org/web/20070622120207/http://nyc10044.com/timeln/timeline.html

New York, NY, although it is often considered part of Queens. Queens nieghborhoods, although part of New York City, are often written out instead of Queens, for example, Forest Hills, NY, so something addressed as Roosevelt Island, NY 10044 would make it there as well.

If you are sure of the ZIP code, it is never necessary to write the city name or even the state. ALL mail sorting is done by the ZIP. The city and state are there only if the ZIP is incorrect.

I address nearly all my mail sans city and state.

Just be sure that the ZIP is correct!

As far as the question is concerned...

The default/actual city name in 10044 is New York.

Acceptable/recognized city names in 10044 are Roosevelt Isl. or Roosevelt Island.

Don't use these for 10044: New York City / NY / NY City / NYC

https://tools.usps.com/go/ZipLookupResultsAction!input.action?resultMode=2&companyName=&address1=&address2=&city=&state=Select&urbanCode=&postalCode=10044&zip=