I know of two Abilenes: one in Texas and one in Kansas. I know that the one in Texas was named after the one in Kansas, because at that time (long ago) Abilene, KS was a big cattle shipping hub. Even back in the 1800s, this was the destination for many of the historic cattle drives; that is, the cattle would be driven to Abilene where they would be loaded onto the trains to be shipped all across the country.
I have never seen Abilene, KS, so I can't vouch for its prettiness. I did live for two years in Abilene, TX, and I can say that it is certainly NOT the prettiest town I have ever seen. So maybe they wrote this about the one in Kansas. Or maybe they just liked the sound of the word "Abilene" and decided to use it for a song.
Anyway, I've always liked this song. It's fun to sing, and it has a nice repetitive chord progression. I think I'll start doing it at the nursing home. It should go over well there.