Hello and welcome to Apple Support Communities, mac_isikoff,
We understand you're seeing the wrong location shown on the Weather widget on your iPad. We'd be happy to help you troubleshoot this.
You mention you added your own location, but didn't specify if this was from the widget screen or within the Weather app. Use the steps here to change the city shown. If that fails, try removing the widget and then adding it again: Use widgets on your iPad - Apple Support
"Edit your widgets
Some widgets allow you to customize their content. Here’s how:
- Touch and hold a widget to open the quick actions menu.
- Tap Edit Widget
. - Make your changes, then tap outside of the widget.
You can also rearrange your widgets. Touch and hold a widget until it jiggles, then move the widget to where you want it to go. As you move the widget, apps and other widgets on your Home Screen rearrange to make room for it.
To delete a widget, touch and hold it, then tap Remove Widget. Tap Remove to confirm."
Regards.