Hi. You might just have the wrong location settings set. Oh, and you didn't say which version of iOS you're running, but, given the notification center mention, I'm going to assume its 5.0.1...
Tap on the weather info on the notification screen. The stock weather app will open. Tap on the exclamation mark icon in the lower right and do one of two things: (1) Turn "Local Weather" on or (2) tap the plus sign in the upper left to add a zip code for which you want to see weather.
Please note that these are exclusive to each other - you can't have local weather on and a zip code active; it must be one or the other.
Hope this helps. Please let us know how you get on.
Marilyn
