Weather widget behavior lacking

I need my weather WIDGET to display minimal temperature and precip and time for the location I've selected, and not just the present position it detects. I have tried over a dozen new wx apps, free & paid, highest & moderately rated, to no avail. Sometimes in the app it will let you keep several locations stored, but the widget will only show present position & that time zone's time; or, whatever location you initially selected when you instantiated the widget.
On the phone I'm discarding (SCH-I545/verizon) the built in "weather" widget-only app works perfectly but that's not available.

I can do this with Beautiful Widgets Pro. Just set it up. Then if you want to change the location, tap the widget to show the forecast, then tap the location name at the top. It will bring up a sidebar with the option to choose the location whose weather you want to display. Top of location list will be present location, then the rest of the saved locations follow.