Develop standard method to access test data files #6683

In #6664, there was some discussion how to access test data in documentation. It would seem handy to have a general method. In #6664 (comment), I wrote and suggested:

I think there is a general question here of how to access test data files. In a package of my own, I "solved" it by having an __init__.py for my data directory that defines variables that hold the paths to the various files, which then can be imported [1]. Not sure that this scales to all of astropy, but I think that instead of

fits_scaledimage_filename = fits.util.get_testdata_filepath('scale.fits')

it is clearer what happens if one sees,

from fits.test_data import scaled_image_file

Another advantage is that it allows the test data files to have docstrings, which can be typeset with sphinx (and I guess with suitable cleverness be made part of the instance).

[1] https://github.com/mhvk/baseband/blob/master/baseband/data/__init__.py