Billy Joel’s The Ballad of Billy the Kid (youtube) visualised:

From a town known as Wheeling, West Virginia
Rode a boy with a six-gun in his hand
And his daring life of crime
Made him a legend in his time
East and west of the Rio Grande

Since Billy Joel hasn’t specified the exact area in which Billy the Kid was a legend in his time, I have assumed the drainage basin of the Rio Grande. There is a large uncertainty associated with this.

Well, he started with a bank in Colorado
In the pocket of his vest, a Colt he hid
And his age and his size
Took the teller by surprise
And the word spread of Billy the Kid

I have chosen the First Mountain Bank, Leadville, CO as Billy the Kid’s first crime. I expect he’d travel there along the route of I-70, as otherwise crossing the Continental Divide in Colorado is tricky, even if you have a Colt / six-gun, which they all do in Leadville.

Well, he never traveled heavy
Yes, he always rode alone
And he soon put many older guns to shame
And he never had a sweetheart
And he never had a home
But the cowboy and the rancher knew his name

Well, he robbed his way from Utah to Oklahoma
And the law just could not seem to track him down
And it served his legend well
For the folks, they’d love to tell
‘Bout when Billy the Kid came to town

I’ve planned his route from Utah, Utah to Oklahoma, Oklahoma, as they are both so good they named them twice. There are three sensible routes (suggested by Google). It seems most likely that he would rob his way via the region in which he became a legend in his own time, but the I-70 route would be more familiar and he could pop into his bank for another withdrawal.

Well, one cold day a posse captured Billy
And the judge said, “String ‘im up for what he did!”
And the cowboys and their kin
Like the sea came pourin’ in
To watch the hangin’ of Billy the Kid

Billy Joel then goes on to talk about another Billy, but that’s a different story.