Göbekli Tepe sits among low rolling hills a couple of kilometers outside of Şanlıurfa. You can see a village in the distance, but the site feels remote and desolate. You park your car in a small lot near a pair of resting camels. Despite a couple of Turkish-German-English explanatory signs, there is little real tourist infrastructure and no one to charge admission.
Fifteen years ago, Göbekli Tepe was unknown. Fifteen years from now, it may well be more famous than Stonehenge. If only we'd come before National Geographic's June 2011 cover story, we could've said we'd come before it was cool.
Göbekli Tepe is the achievement of nobody-knows-how-many Neolithic people who built, tore down, and rebuilt the site over centuries, until the whole area was deliberately buried in sand and forgotten 10,000 years ago.
Perspective note: nearby Şanlıurfa is believed by the faithful to have been the hometown of the biblical Abraham. Going by the oldest estimates for Abraham's year of birth, at that time well over half as much time had passed since Göbekli Tepe's abandonment as now. And that's since the site's abandonment, not its original construction.
Göbekli Tepe is over twice as old as some religious scholars maintain the world is.
Not being an expert, I can't say much about the site's significance. I recommend you read the National Geographic article, or Newsweek's article, or the shorter but to-the-point The First Post FAQ. But I do know that archeologists believe they've just begun to scratch the surface of the site, and there is much more hidden underground.
To be honest, there isn't a huge amount to see at the site right now. We thought it was well worth the trip, but mostly for the historical significance and the desolate otherworldly atmosphere. But this is a site to watch.