I found a cool website, or at least one that's cool to a useless information geek like me. At:
You can drag the top map to wherever you want, and the lower map responds, showing you what is on the very precisely opposite side of the earth. That is, if you were to dig a hole straight through the center of the earth, this is exactly where you'd come out. Most sites come out in the middle of one ocean or another, of course. If you happen to BE in the middle of the ocean, of course, you might come out on land. If you dig in Hawaii, you come out in Botswana and Namibia.
Some other locations also come out on land. For example, my friend Bill http://aotearoadreaming.blogspot.com/
relocated to Wellington, New Zealand, and if you dig there, you come out in Spain, at the town of Alaejos. They should set up a sister cities program with them. They could each set up a directional sign with an arrow pointing straight down and the other place's name, and the legend: 12,742 kilometers or 7,917 miles. That is, of course by the shortest route possible, but I wouldn't recommend traveling that way. You can't possibly be further away from home, and still be on the planet, if you're at your antipode, which is an unsettling thing to me.