On mobile so this isn't going to look totally pretty. Zhang Qian was a court traveler in the Han Dynasty era credited with opening the Silk Road. Prior to that the Chinese had no clue that they weren't alone in the world. John Keay compares the Chinese "discovery" of India as being similar in psychological, social, and economical impact as the European "discovery" of America.

http://en.m.wikipedia.org/wiki/Zhang_Qian

Xuanzang (aka He Of Many Names) was a Tang era monk who developed a desire to travel to India to recover proper Buddhist scriptures where China seemed to lack any originals or favorable translations. Naturally he took the aforementioned Silk Route there and (AFAIK, someone please correct me if I'm wrong) he traveled back via Sri Vijaya. His journey is epically famous and popularized in the Ming-era novel "A Journey to the West."

And later in Dragon Ball Z.

http://en.m.wikipedia.org/wiki/Xuanzang

I'm particularly fond of the below article about the Korean imagination of Tibet because it shows that even in the range of local myopeia, there was still this concept of a Buddhist holy land as far away as Korea and Japan. And that monks from these places were traveling there. The Silk Route's largest expert to Eat Asia was by far Buddhism. John Keay's "China" (for all is faults) does well to illustrate just how antithetical to the Confucian mind Buddhism was before the Tang era. So consider the challenge of penetrating that society to reach even farther lands and then be attractive enough to pull those far away people out of their comfort zones to lands that aren't even mapped. Look up "Buddhism in [Country]" and you're bound to find Marco Polo types - monks and otherwise - journeying to India.

http://journals.ub.uni-heidelberg.de/index.php/transcultural/article/view/9128/3102

Finally aside from Zheng He (who was more of an Asian da Gama) who I'm surprised hasn't been brought up yet, there's the fascinating tale of Yamada Nagasama. He was A Japanese adventurer who left his home in the 16th Century to wind up in the court of the Ayyuthaya Kings and even became the governor of a Thai province.

http://en.m.wikipedia.org/wiki/Yamada_Nagamasa

And this doesn't really touch on the steppe lords: Huns, Mongols, Turks, all of whom traveled father distances well before Marco Polo considered the idea.

Matteo Ricci (1552-1610) was a Jesuit who went to China and lived there 27 years until his death. He was able to penetrate into the highest levels of the court and became an adviser to the emperor, thanks to his the knowledge, technology, and maps he brought to China.

One interesting thing he did was he tried to say that Christianity and Confucianism were very similar, in an attempt to convert the Confucian upper crust of society. For example, Confucians had a Lord in Heaven, so Ricci was like "we have a Lord in Heaven too." However the Chinese scholars were pretty savvy gents and Ricci didn't have much success. They poked holes in a lot of Christian beliefs and the Jesuits didn't have much success with converting that class of people.

For example, the scholars wrote (paraphrasing) "Why did the Lord in heaven have to send his son to earth to die to wash away the sins of man, why could he not just wash away the sins of man from his seat in Heaven."

And like the Muslims, they also tore apart the monotheistic god that has 3 gods inside of it (Father, son holy ghost). They did not see the logic in that. That was a fun document. Can't remember the name but it was 30 or so point form criticisms of Christianity from what understanding they had of it, which was not the greatest.

Father Matteo journals can be found, but I have not read them so I cannot comment on them. They are likely very interesting though.

EDIT: Just found a book available online through my university database. Matteo Ricci Written By: Fontana, Michela. It looks to have very specific short sub chapters if you want to skip to parts of interest.

A related question: How do we know about Rabban bar Sauma's journey from Beijing to Paris? From what I know it doesn't sound like it wrote it down himself (though I may be misinformed), so who did?