Even before the Meiji Restoration, Japan realized it was facing a situation in which it would either be colonized by the West or it could compete with the West. After the Meiji Restoration, a delegation was assembled by the government to travel to America and Europe to study their industrialization methods for Japan to use in it's own industrialization. I'm on my mobile and don't have the book near me at the moment, so I will post a source when I'm able to. Many of the delegates reported being amazed at the West and industrialization process but also worried over how much Japan lagged behind the West and how vulnerable it was after centuries of stagnation. This realization and the urgency with which the delegation urged the Meiji government to modernize resulted in heavy investment in the industrial manufacturing sector.

This is, of course, a special case but travel before the Meiji Restoration was impossible and travel after it was slow to start until the political and economic situation stabilized. I'm not sure if this is relevant, but Western styles of clothing, building, and decorating became popular among the elite (who would have had the funds to travel). While much of it was from imports and the desire to show how modern one was, some of it was items they had picked up from their travels.

Sorry I don't have more sources for the second half of your question.

Edit: source: Japan: A Modern History by James L. McClain. My focus is US labor and environmental history. I had several courses on Japan while earning my degree, but I am by no means an expert. I will continue to try to find some sources for OP to read.

I believe I can partially answer the second part of your question, with regards to how the Japanese people viewed Westerners at the time (although I know I'm a little late).

During most of the 19th Century, most of the Japanese had a very limited knowledge of Western culture. Plenty of them who had not visited Europe or America only had brief glimpses of them on which to base their opinions.

This woodblock print from Utagawa Yoshikazu is from 1861 and was distributed in news publications in Yokohama, Japan, a city near Tokyo (Edo at the time). Yokohama was established in 1858 as a port town in which foreigners, primarily Europeans and Americans, could conduct business.

The Japanese were fascinated by these immigrants, and these prints depicting their odd fashion and culture grew very popular. But in its early years, most of the settlers in Yokohama were wealthy, male traders. The Japanese, seeing how the upper class of the Western world dressed, assumed this to be everyday wear, which is why the individuals in this print are shown to be so overdressed for the simple task of baking bread.

Additionally, there were very few women at the time who lived in Yokohama, so the Japanese had even less knowledge of how they dressed. The artists of these prints would often times mimic pictures of women's clothing from Western publications in order to show how they dressed and behaved.

But going back to your initial question, even as late as the 1860s and 1870s most Japanese had very little knowledge of Western culture beyond publications that they had at hand. The artists of these prints depicting Western culture had very little first-hand experience with Americans and Europeans, and for the average citizen of Japan, these images would be about the only knowledge they had of the West.

These missions from Japan to the West and around the world were some of my earliest research as a Masters student, many years ago. You can find some of the primary sources, such as the autobiography of Fukuzawa Yukichi, who traveled to the US in the 1860s, and the much larger, state-sponsored Iwakura Embassy in the 1870s. Their official scholar, a man named Kume Kunitake, wrote an extensive, multi-volume report that is a fascinating read. Indeed, Kume probably saw more of the West than most Westerners. If I recall correctly, their large party traveled across the Pacific to San Francisco, took the transcontinental railroad across the US, travelled to Britain, France, Germany, Austria, and Italy, then through the Suez Canal to India and then home via Singapore and Hong Kong.

Their reactions differed, as you might expect. Yukichi was an unabashed proponent of opening up to the West and copying its ideas and technologies, and one thing I remember clearly from his autobiography is that while he was terrified while crossing the Pacific, he expressed supreme confidence in his ship because it was a steamship of Western (American?) design and construction. Kume's views were more nuanced. His embassy was tasked with essentially surveying the West, including their politics, economics, culture, and customs, with the goal of identifying things that Japan could adopt or adapt for their use. In many cases, they were astonished by the scale and grandeur of European wealth, but equally so by European poverty. They were awe-struck by the industrial districts of northern England, a place that must have struck them as utterly alien. At one point Kume remarked that his party saw nothing growing anywhere, and nothing coming from the ground except coal and iron. This landscape must have seemed simultaneously hellish and "modern," and perhaps even inevitable given that they understood fairly well that such transformations of nature were the foundation of military and economic strength.

Kume's description of the West suggested an acceptance of several elements as necessary for existence in the modern world, in particular industrial technology, a market economy, and a powerful state based on national identity. Europeans at the time discussed virtually everything in terms of national characters, and this particularly evident to this group as they traveled to different places and had such ample opportunities to compare things in national terms. This even extended to their ideas about plants: at one point, while touring the pine forests of Scotland, Kume compared the ramrod-straight pines they saw to British personalities and British industrial society, while the pine trees he was accustomed to seeing were curved.

Kume and his companions found this national discourse appealing: it suggested that it would be possible to adopt many of the institutions, practices, and technologies that made Europeans so powerful, while still preserving their inherent Japanese-ness. In other words, it was a kind of intellectual grounding to the notion that they must adapt to geopolitical realities of the late Victorian world, but that it was possible to do so on their own terms. Their whole mission was in part premised on that, so it's not surprising that they found evidence to support that.

A further point on what they saw and what impressed them was Europeans' cooperative institutions. As they arrived in new cities, they were frequently met by chambers of commerce or other elements of civil society that suggested to Kume that Europeans had a particular capacity for working together. This was important for two reasons. First, it was salient in light of the recent civil war in Japan; if Europeans were the powerful people in the world and one of their unique characteristics was to work together, then Japanese people had better learn to do the same. Or, put another way, get on board with the new Japanese government and its goal to transform the country. Second, it to an extent concealed the atomizing tendencies of a market economy and market-based society. It's ironic that Kume would conclude that Europeans were so cooperative, since one of the foundations of European wealth at the time was market competition. By observing and then emphasizing cooperation in his report, Kume implies that markets can be adopted but their potentially negative effects mitigated.

There's a considerable amount of scholarship on this; I can look up work for you if you'd like, or I can post the paper I wrote. That'll take a while to dig out, but it's doable.

Are you familiar with "The Three Kichis?" In 1834, a three Japanese fisherman Iwakichi, Kyukichi, and Otokichi, were blown off course. They eventually wound up 5000 miles away in what is now Washington State. They were seized by Indians, rescued by the British, and sent to London.

From London, they were sent to Macao, were the British essentially abandoned then. A few years later, an American trader attempted to repatriate them to Japan, only to be fired upon. They were then sent back to Macao.

It's unclear what happened to Iwakichi and Kyukichi. Otokichi embraced western culture. He married a British woman and became a Christian missionary. He changed his name to James Matthew Ottoson (from "Oto-san"). He refused Japanese repatriation 19 years later.

Source: http://www.historylink.org/index.cfm?DisplayPage=output.cfm&file_id=9065

How many other 19th centuries were there I wasn't aware of?