Everywhere is the center of the universe. Or at least it seems that way sometimes. No matter how isolated a town is from the rest of the world, they're always going to think about places and events in relation to where they are. Any city of any size will, however rightly or wrongly, think of itself as the hub of the county, the region, the state, the country, the world. Everything goes through them (solve for value of "everything").
As such, it will sometimes happen that one of these places will construct a road sign or a compass or a globe or some sort of large-scale 'You Are Here' sign.
For many countries, this takes the form of something Wikipedia has blanket-referred to as Kilometer Zero. Kilometer Zero is a marker or monument located somewhere in the country- typically the capital, but not always- from which all distances in the country are intended to be measured.
France's Kilometer Zero is this marker in front of the Cathedral of Notre Dame. Spain's is this marker in Madrid's Puerta del Sol. Indonesia's is this building on the west coast of the island of Sabang. Ukraine's is this monument in Kiev. Canada's is the western end of the Trans-Canada Highway on Vancouver Island, British Columbia.
The United States has a Kilometer Zero, called Zero Milestone. It was created in 1923, sitting within eyesight of the White House. However, in practice, it only serves as Kilometer Zero for Washington DC. Everybody else does their own thing. Mile markers might measure the distance to the county line or state line. Highway distance signs have no definitive answer I could hunt down. When looking for what a sign signifying distance to any given city uses as its point of reference, I came up with the post office (though which one?), some other public building, 'a point close to the center of town', and 'the edge of town'. You're on your own for that one.
Italy's current Kilometer Zero is the top of Capitoline Hill in Rome. Back in the days of the Roman Empire, though, they used the Milliarium Aureum, a golden milestone (that's the translated Latin) with gilded bronze finishing. It's thought, but not confirmed, that the Milliarium Aureum had listed on it distances to all the major cities in the Roman Empire (hence the term 'all roads lead to Rome').
Not many modern Kilometer Zeroes list city distances. That role has largely been relegated to signs that look like this one at Lake Louise Ski Resort in Alberta:
Those are the fun ones, incidentally.
But the undisputed Kilometer Zero champion has to be- and if you've ever driven in South Dakota, you know it already- Wall Drug. It's not every tacky tourist trap that can get itself a sign in Amsterdam. Or Antarctica. Or Bagram AFB in Afghanistan. Or a sign that tells you about their other signs in Kenya and London.
Or this blog.
It's 676 miles to Wall Drug, South Dakota.