Where do I end up if I dig straight down?

Nice. It's interesting to see that pretty much the entire U.S. is opposite ocean. For the 50 states, the only exceptions seem to be the northernmost tip of Alaska, which is opposite part of Antarctica, a little bit of northern Montana, north of Great Falls, which is opposite the catchily named "French Southern & Antarctic Lands" island, and the islands of Hawaii, which are mostly opposite Botswana, with just a little bit being opposite Namibia.

BTW, a pedantic point: If you dig straight down, you end up at the center of the Earth. If you keep going from there, then you're digging up.

EDIT: The area just southeast of Lamar, Colorado is opposite a tiny island called "Ile Amsterdam". And southwest of Cheyenne Wells, Colorado, you are opposite an even tinier island called "Ile Saint-Paul".

The name for the point directly opposite the globe from another point is called antipodal. Thus, ggchappell's observation means that Cheyenne Well, Colorado is antipodal to Ile Saint-Paul.