If you want to dig a hole straight through the Earth to China, start digging in Argentina. This is one of the few places on land in which the antipode is not located on an ocean. With most of the Earth's surface covered by water and most of the land area in the Norther Hemisphere, this is not really surprising.
Ze Frank has a project to create "Earth Sandwiches", which is created when two slices of bread are simultaneously placed on opposite sides of the Earth. To assist this project, his website has a Google Maps tool that can display the antipodal spot of any place mark.
There is an area in northern Montana that is opposite from the Kerguelen Islands in the South Indian Ocean. There is also a small island, Île Amsterdam, antipodal to spot southeast of Lamar, Colorado and Île Saint-Paul, which is opposite from Firstview, Colorado. These are the only land areas antipodal to the Lower 48 United States.