In iOS 6, how can I convince Siri that New York City is not in Texas?
This is a legitimate bug with Siri: http://www.macrumors.com/2012/09/24/siri-delivering-wrong-weather-forecasts-for-common-city-names/

The bug has to be fixed on Apple's end (or Yahoo's, or wherever exactly the problem is occurring).

But you can work around it temporarily by asking for the weather in "Zip Code 10028" (or whatever).  Note that you seem to have to say "Zip Code" - just using the number doesn't seem to work.

That's a bit surprising that you're seeing it now since it first popped up almost three weeks ago – you'd think they would have fixed it by now. I guess all you can do is wait and it'll resolve itself at some point.