For users who live in New York, NY, asking for weather in "my area" doesn't seem to help either, and only by specifically using their zip code can they get accurate weather. However, it's not just New York that is running into issues. Another user lives in Richmond, Virginia but Siri is delivering weather for New Richmond, Ohio. Weather requests for Carrollton, Texas are showing up as Carrollton, Indiana. Asking for weather in St. Louis, Missouri gives weather in St. Louis, Georgia.
A number of threads on Apple's official support forums also report problems, with no apparent resolution. The issue appears to be on Siri's end, and cannot be fixed by the user. We have reached out to Apple for more information.