I can’t get rid of the weather that shows up by default on my screen. It is not a town I live in.

Perhaps your refer to a Weather Widget. Touch-and-hold (i.e., long-touch) the Widget…

• If you wish to remove the Widget in its entirety, select Remove Widget.

• If you wish to change the displayed location to another city, select Edit Widget, tap Location then select the preferred city or Current Location.

If instead you are attempting to change the list of cities of interest within the Weather App itself - open the Weather App; within the associated sidebar you will see a list a locations for which a forecast has been configured.

To Add a location, use the search field to enter a town/city of interest - then tap the most appropriate candidate from the list - and finally tap the Add button.

If you wish to remove a location from the configured list, at top-right of the Weather sidebar, tap the More (“…”) icon - and from the menu tap Edit List.  Each of your configured locations will now have an associated red “-“ button. Tap the button for each location that you wish to delete from the Weather App. When you’re finished, tap Done.