It's one of those pithy little quotes which reveals so much about our two cultures. The average Briton considers anything more than a 45 minute trip a bit of a schelp, whereas Americans will seemingly drive half a day just to get some ribs from that one place they like. Conversely, I went to school opposite a church which pre-dated Columbus's invasion of North America - and I doubt that was the oldest church in the town!
But who said it first? Oh, there are a variety of sites online which will swear that it's a modern author. But let's see if we can find a quote from the last century.
Back in 1999, Neil Gaiman was interviewed in Locus Magazine and said:
England has history; Americans have geography. Which goes back to that joke, ‘America is a country where 100 years is a long time, and England is a country where 100 miles is a long way.’ Both of those things are true on many levels. There really isn’t a great English road trip tradition, because in three or four days, you’ve done it all. Whereas in America, the idea of the road trip is this magnificent long slog.
So it was already an establish trope by the tail-end of the millennium - as can be seen in Billboard Magazine's October 1998 edition.
Diana Gabaldon published "Drums of Autumn" in 1996. She's often cited as the origin of the quote.
Travelling back a bit further, there's a Usenet post from 1995 where 'Mike "from the US, but my wife is from Scotland" Bartman' says:
It appears that the difference between the US and the UK is that in the UK 100 miles is a long way, and in the US 100 years is a long time... ;^)
There's quite a few Usenet posts with that phrase, but I couldn't find any before the mid 90s.
In 1992, Benjamin Jones wrote a column in "EUROPE, The Magazine of the European Community" (ISSN 0191-4545)
But the earliest I can reliably trace it back is a book from 1991 called "The Changing context of social-health care : its implications for providers and consumers". It in, Emily Friedman wrote a paper called "Patients as Partners: The Changing Health Care Environment" which talks, in part, about the litigious nature of American consumers of health services. She writes:
Who was this "Simon"? Is he a real or imagined interlocutor? Did he originate this mot juste? Given the passage of time, it's probably impossible to find out.
That claims to be from 1988 - but there doesn't appear to be an archive of the
HUMOR@UGA.CC.UGA.EDU listserve that I can find.
However, it does turn up in the venerable TextFiles:
It looks like "Fraser" at DEC sent that via UUCP to (for those of you not familiar with the now obsolete "Bang Path Notation) funny at looking via University of Waterloo's math department. Whereupon Brad Templeton probably re-circulated it to Usenet's "rec.humor.funny".
And that's as far back as I can trace it. Early Internet history is either mouldering on a set of tapes somewhere or completely lost. Google Books and Archive.org don't show the phrase appearing any earlier. But perhaps your research skills are better than mine?
Can you find an earlier reference? If so, please stick a comment in the usual box.