Hi Alan,
Did you get the error like this?
If yes, as far as I know, this issue may be caused by some factors.
One:
Visio 2013 was not activated. Please try to activate it.
Two:
Please click "Categories" to check if the templates are existed. If we still can't see them, I'm afraid the default build-in templates are corrupted somehow and we need to copy a healthy one from another computer.
Path: C:\Program Files (x86)\Microsoft Office\Office15\Visio Content\1033 (32bit)
C:\Program Files \Microsoft Office\Office15\Visio Content\1033 (64 bit).
Hope it's helpful.
Regards,
George Zhao
TechNet Community Support