If you drilled a straight tunnel through Earth’s center from Los Angeles (34.05° N, 118.24° W), you would emerge in the Indian Ocean, roughly 12,430 miles (20,000 km) away. The precise antipodal coordinates are approximately 34.05° S, 61.76° E—about 1,000 km southwest of Australia and 1,500 km southeast of Madagascar.
Nothing but deep ocean (depth ~4,000 m). The nearest landfalls are the French Southern and Antarctic Lands (Îles Kerguelen) to the south and the Australian territory of Heard Island to the southeast. No commercial shipping lanes or flight paths cross this remote sector regularly.
So the "farthest point from Los Angeles" is a patch of featureless sea—Earth’s ultimate nowhere.