This is not an answer to why China wasn't the first to discover America. Maybe an expert can answer that. However I just want to point out that the premise of the question is incorrect. According to Google the distances are as follows:
Mainland Europe is quite a bit closer to America than China.
Aside from the geographical gaffe pointed out by /u/ParallelPain, a key problem with the question is that it assumes that the 'discovery' of the Americas (in quotes because there were already plenty of people already there) was in some way something that had to happen – that somebody from the Old World would inevitably have sought to locate and potentially conquer a hitherto unknown continent once they had the technology to achieve the voyage necessary. This was simply not the case. As many of us will be aware, the 'discovery' of the Americas by Columbus was not premeditated, but rather the product of a search for a shortcut to Asia, a search driven by competition between Spain and Portugal for control over the valuable Spice Islands, and potentially lucrative conquests further afield in the Far East.
This was in many ways a contingent affair: Portugal and Spain were maritime powers, furnished with a combination of technologies that gave them the means to travel long distances efficiently (square-rigged sailing ships); to overcome local defences (portable gunpowder weapons such as arquebuses); and to hold these conquests with relatively little investment in manpower (bastion forts). While these technologies made such conquests viable, their possession by two separate powers also created motive for competition, as they sought to most quickly and effectively exploit these technologies in pursuit of the exploitation of distant economic resources. Moreover, Portugal and Spain knew that there was something in Asia that they would want to find before the other did.
The point of comparison is of course the voyages of Zheng He in the early part of the fifteenth century, whose ships ranged as far west as the ports of Mogadishu in Somalia and Jedda on the southwest Arabian coast. As with the Portuguese and Spanish expeditions, Zheng He's voyages were undertaken to achieve geopolitical aims by securing the allegiance, either through persuasion or coercion, of various states in Southeast Asia and on the coast of the Indian Ocean. Ming China was basically trying to achieve hegemony over the same general region of the world. Ming China had relatively little interest in Europe, as they likely knew little about it; if they did, it is improbable that they would have wanted anything from it; and even then, there was no real local competitor to make such an investment seem attractive.
Why the disparity in interest? On a purely economic front, it seems Europe wanted more from Asia than Asia wanted from Europe. Culturally, narratives of places like India and especially China as far-off, mysterious lands of great riches (e.g. Marco Polo's travelogues) had circulated for some time in Europe (it's worth noting that when Columbus landed in Cuba, he thought he was on the coast of China, not India); such narratives of Europe did not exist for China.
We must also add to this a technical aspect: junks were not particularly efficient in terms of their handling, but rather built to be economical. Junk voyages were usually quite short, with regular maintenance stops, and we see in the case of the Zheng He voyages that the treasure fleets had several consecutive ports of call, around 1500 miles apart in the case of the seventh and farthest-ranging of the expeditions. The longest single leg of the seventh Zheng He voyage was Calicut to Mogadishu, a route of roughly 2300 miles, or about a quarter of the distance from Shanghai to San Francisco. Simply put, the treasure fleet was probably not capable of making a trans-Pacific journey, especially without certainty of being able to resupply for the return voyage. But this technical aside should not be treated as the be all and end all, because the real point is the one made above: European maritime powers had reasons for ending up in the Americas that were not shared by the Chinese.
Or, to put this somewhat snarkily, Europeans ran into the Americas while trying to get to Asia faster. The Chinese were in Asia to begin with.
Hey there,
Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.
If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!