China's easternmost location is at the intersection of the centerline of the main channel of the Hei Long Jiang and the Ussuri River;

China's northernmost location is on the centerline of the main channel of the Hei Long Jiang at the northern end of Mohe County;

China's westernmost location is on the Pamir Plateau;

China's southernmost location is at Zengmu Dark Sand in the Nansha Islands.

China's easternmost city, Fuyuan;

China's southernmost city, Sanya, Hainan;

China's northernmost city, Heihe, in Heilongjiang province;

China's westernmost city is Wuqia, Xinjiang.

A more specific answer:

The westernmost part of China's territory is in Xinjiang's Wuqia County on the Pamir Plateau, specifically at about 39 degrees 15 minutes north latitude and 73 degrees 33 minutes east longitude, about 25 kilometers southwest of the intersection of the borders of China, Tajikistan, and Jilin province, where there is a snow-capped peak that is more than 5,000 meters above sea level.

The northernmost point of China's territory is in the territory of Mohe County (city) on the Heilongjiang River, but not in what is commonly thought of as the town of Mohe, but in the town of Usuli, more than 60 kilometers east of Mohe, where the northernmost latitude of the main channel of the Heilongjiang River is 53 degrees, 33.5 minutes north latitude. The northernmost latitude of the town of Mohe is 53 degrees 30 minutes north.

The easternmost point of China's territory was previously thought to be the confluence of the main channels of the Heilongjiang and Ussuri rivers, but that has changed since the Russian-Chinese agreement to divide Heixiazi Island.

Until the two sides complete the demarcation of Heixiazi Island, there are two possible candidates for the easternmost part of China's territory: (1) it could be on Heixiazi Island; and (2) it could also be in the heart of the Ussuri River more than 60 kilometers south of Heixiazi Island (at longitude 134 degrees, 46.5 minutes east), with the nearest town being Haiqing Town in Fuyuan County.

China's southernmost territory is theoretically Zengmu Dark Shadows (3 degrees 51 minutes north latitude, 112 degrees 16 minutes east longitude), but is a submerged reef shoal 20 meters underwater.

The southernmost of the Spratly Islands' reefs that can be exposed to the water (I don't know its name) is located at 7°22'N, 113°50'E. Unfortunately, it has already been seized by someone else (probably Malaysia) and has a 1.5-kilometer-long runway airport.