It has recently occurred to me that all the famous universities in Japan are relatively new. I looked up and apparently the oldest university in Japan was built in mid XIX century. It seems strange to me given that most European countries have universities dating back more than 400 hundred years, some countries like UK and Italy have universities as old as XI century. Japan is a pretty old country with a long and rich history, so why desn't it have much older higher education institutions? Or did they simply not survive until now?
That's primarily because the concept of a "western" University is not entirely translatable to Japanese society pre-Meiji Era. The same could be said about academies and schools within pre-20th century China.
This is not to say that there was no higher education in Japan, but rather that the education system in Japan until the Meiji Era (1868 onwards) was revolved primarily around the establishment of a "Confucian" bureaucracy and education. Though I am hesitant to use "Confucian" as it is not the most descriptive term, essentially the governmental system and civil service examinations within Tokugawa Japan served as institutions of higher education. Again it's not that Japan (as an entity) did not have higher education, as civil service examinations were not only academically rigorous but required an extensive knowledge of philosophy as well.
I suppose the best way to put it is that there was academia and institutions of higher learning, but it simply wasn't named "university." Higher education and a scholarly literati not only existed as a class in Japan but also became the administrative body that constituted essentially all of the bureaucracy and officials within the administration of Tokugawa Japan. That said I would much prefer /u/AsiaExpert to weigh in on this as my knowledge of pre-meiji Japan is not the most accurate.
Literacy levels had peaked by the Tokugawa era, they were possibly in the top three in the world for the period. The lowest figure I've seen is 40% for men, and 10% for women. Generally, high level samurai were privately tutored or they attended han academies (藩校 or hankō), based on the Chinese Confucian academy, shuyuan. The hankō were generally rural, owned by the Daimyo of the domain, and were created with the aim of educating the children of the Daimyo and his retainers. Samurais were only 5% of the population, but had nearly 100% (both male and female) literacy, according to Hane Mikiso (he doesn't source any statistics however). Lower level samurai were generally educated at Buddhist/Shinto temple institutes (寺子屋 or terako-ya), as well as well-off peasants/merchants who could afford it. The terako-ya, unlike the hankō, were urban, and private - owned and controlled by the temple where it was located.
Whatever educational culture Japan had during the pre-Meiji era, it was based on Chinese and Korean educational systems. The Japanese did make strong contacts with Europeans during the sengoku jidai, the period of civil war following the fall of the Ashikaga shogunate (1467 – 1603). However, this was mostly about trade - Japanese Daimyo wanted to purchase advanced firearms and cannons, whereas Portuguese missionaries wanted to spread Christianity. The English and the Dutch got involved when they saw an opportunity to remove Portuguese and Spanish influence from the region. This period of foreign influence was very short, and had no influence on the region, apart from a few Japanese being taken to Manilla and Goa to become Franciscan friars and priests.
After the Tokugawas united Japan and ended the sengoku jidai, they had seen the introduction of firearms and Christianity as destructive to the nature of Japan, and hence introduced the policy of Sakoku (鎖国 - closed country). All foreigners were expelled, and the only trade was with the Dutch at Dejima island and with the Chinese via the Ryukyuan kingdom. Whatever knowledge of the West that developed during this period, it was through Dutch studies (蘭学 or Rangaku). Although repressed at first, Rangaku was somewhat encouraged at terako-yas throughout Japan (the hankō, on the other hand, only focused on Confucian works).
After the Meiji restoration, change of the Japanese educational system on Western lines was of primary importance to the new rulers of Japan. The traditional educational mechanisms were abandoned, and an educational system was introduced - initially based on the American pattern, later on German (as the Meiji leaders realised the American pattern during that time was not uniform and haphazard). Thus, the first Western-style universities emerged.
Now that my interest in Japanese educational history has been rekindled, I might pop by at the school of literature, language, and culture at my university today and find out just how long terako-yas and hankōs survived, and if any still continue to exist today which have other functions, such as educating priests.
Edit: Didn't need to do that. I just read about the Education System Order (学制 or gakusei) in 1872. It had officially shut down all traditional schools and made primary schooling compulsory. Although if I can recall what I had read last year, much of the early school teachers were still priests from the terako-yas, and former lower level samurai. Then, the government had started to establish teacher training institutes with foreign help.