Had the same problem with the clock widget. The difference is tapping the widget or tapping and holding the widget.
If you tap the widget, a list of cities opens. Initially it's set to Cupertino. You can add/delete locations. However, when you close that window, the widget still shows "CUP" time.
Try this instead: If you press and hold the widget, a little menu opens. Select "Edit Widget", this will bring up a place to select a city location. initially you will see Cupertino listed. Select it and choose a new city. Close the app (home button or select outside of the open window) and viola, the new city is shown in the widget.