Apple - Location in Weather Widget is Wrong

Go System Preferences > Security & Privacy > Privacy [tab]
Uncheck and recheck 'Weather' and it's back to normal

See below img

Press the i icon in the top right of the screenshot you provided. There you can change the location for weather. Edit

Did a quick search and it seems to be a bug in yosemite. Found a french website with a solution, link . it seems that the location for you weather is stored in ~/Library/Containers/com.apple.ncplugin.weather. I don't know if this is a temporary fix

Open up System Preference, go into the "Security" pane, and then, within "Location services" check whether the weather widget is allowed to get your current location.

If it is currently checked, and your location is still not correct, uncheck and re-check it again. Note that you might need to unlock the preference pane by clicking on the lock icon in the lower left corner first.