China:

The "The Tribute of Yu" (Yugong 禹貢) chapter of the Shangshu details the story of the culture hero Yu the Great controlling the flood waters and bringing order to the world. The text describes Yu dividing the land into Nine Provinces (jiuzhou 九州) by reclaiming the land from the floodwaters. This idea of Nine Provinces was apparently then developed by Zou Yan (f. 250 BCE), who saw the Nine Provinces of what we now call China as itself being just one Province within a larger scheme of Nine Provinces (here the word for "province" (zhou 州) might better be rendered as "continent" for the larger group) that covered the entire world (or "all under Heaven"). I say "apparently", because Zou Yan's works only survive in fragments quoted in other texts, and this account of his ideas derives from the later Records of the Grand Historian (Shiji 史記). What we now call China was the Divine Continent, which was in the Red District (chixian shenzhou 赤縣神州). This idea of dividing the world into a 3x3 grid was appealing because there was a number of already-existing 3x3 divisions, including the 3x3 division of land called the well-field system, which was named for it's visual resemblance to the Chinese character for a well (jing 井), and divinatory charts were also divided into 3x3 grids. Moreover the number nine had numerological and cultural significance (see for example the Nine Bronze Vessels jiuding 九鼎).

During the Han dynasty, China was situated, according to this theory, in the southeast corner of the Nine Continents (I'll use "continent" for the larger-scale division to avoid confusion). This was perhaps partly done to allow Mount Kunlun to be central, but it was controversial and was attacked in a number of texts (Wang Chong called Zou Yan's ideas "bizarre"). Part of the reasons for the controversy were the implications of not situating China in the centre, especially regarding the authority of the Emperor.

Perhaps more troubling was the gaitian 蓋天 theory, which used the image of a circular umbrella-like awning over a square-shaped chariot to describe the world. The circular awning described the shape of Heaven, the square chariot the shape of the earth. The theory was troubling because while this part was well-accepted, the theory also said that it was impossible for the Central Plains (zhongyuan 中原, or the Central States zhongguo 中國) to be at the centre of the world, because that centre must be at the Northern Extreme (beiji 北極), which was where the canopy of Heaven rotated over the chariot of the earth. Incidentally, the idea that the earth was square was so persuasive that, despite their sophisticated measurements of celestial bodies, the flatness of the earth was rarely challenged until the Jesuits came to China during the Ming dynasty.

The Han dynasty text the Huainanzi combined Zou Yan's Nine Continents theory with models derived from a text of uncertain date called The Guideways through Mountains and Seas (Shanhai jing 山海經; the title is conventionally translated as "Classic of Mountains and Seas", but a number of scholars have shown that the interpretation of the word jing 經 as "classic" for this text is quite unlikely). In the Guideways, locations are described relative to each other and grouped into mountains, oceans, and "wildernesses" (huang 荒) of each cardinal direction, that are themselves arranged in concentric squares (although this interpretation has been challenged by Dorofeeva-Lichtman). So you had the East Mountains, the West Mountains, etc. The mountains were in the centre, surrounded by a region called "Inside the Seas", which was itself surrounded by a region called "Outside the Seas", then finally surrounding them all was the "Great Wilderness". The further away you got from the centre, the stranger the places and their inhabitants would be (see for instance this interesting fellow).

After the Wang Mang interregnum, the Han capital was now in Luoyang, east of the former capital of Chang'an. Another theory of the world, known as the huntian 渾天 theory, appears to have become popular during this time. It had been around since the Western Han, but the desire to see the capital as central may have boosted its popularity. Huntian theory stated that Heaven is a sphere surrounding a flat earth. This is distinct from the gaitian explanation which saw a boundary between Heaven and earth at the Northern Extreme, whereas huntian describes them as continuous. Most importantly, huntian put the Central Plains in the centre.

At this point I feel like we're getting a bit away from geography proper, so I'll stop there. The TL;DR is that, despite what you might read about China considering itself the "Middle Kingdom" since time immemorial, there were many debates about how to divide up the world and where to locate what we now call China within that. Like most societies, there was a tendency for the ancient Chinese to see themselves as central, but this centrality was also subject to debate. I haven't even mentioned Buddhist cosmology, but for more on that see Janine Nicol's dissertation.

References
Christopher Cullen. Astronomy and Mathematics in Ancient China: The Zhou bi suan jing.
Mark Edward Lewis. The Construction of Space in Early China.
Vera Dorofeeva-Lichtman. "Mapless Mapping: Did the Maps of the Shanhai jing Ever Exist?"
John S. Major. Heaven and Earth in Early Han Thought.
Janine Nicol. Daoxuan (c596-667) and the Creation of a Buddhist Sacred Geography of China: An Examination of the Shijia Fangzhi.
Richard E. Strassberg. A Chinese Bestiary.