Why does my Weather app on my iPad always default to a town I do not live in?

Perhaps your refer to a Weather Widget. Touch-and-hold (i.e., long-touch) the 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 - which should include My Location.

You can add other City locations in which you have interest - or you can arrange or delete locations. To do so, simply tap the ellipsis (“…”) icon - and from the menu tap Edit List. 

How do you have location services set up?

I'm not on my iPad at the moment, but there is that functionality in settings IIRC.