The Dashboard Weather widget might provide information about a city other than the one set in Date & Time preferences. But you can easily adjust the widget's settings if needed.
For example, the Weather widget might display temperature and weather information about a different city of the same name as yours (you might have Austin, TX selected in the Date & Time preferences, but the Weather widget displays weather for Austin, PA; or Sydney, FL instead of Sydney, Australia).
If this happens, change the city in the Weather widget. Just click the "i" button and enter a new city and state, or zip code, in the field. You can also change the temperature display from Fahrenheit (F) to Celsius (C), or vice-versa if you want.