Please see the ACROSS (Archives Cross Boundaries) website, the National Archives Administration National Development Council (government documents), the Ministry of Culture website, and The Church Historical Archives (material on Christianity in Taiwan and the February 28 incident). More information is available below.
The ACROSS website features archives from Academia Sinica (including the archives of the Institute of Taiwan History, the archives of the Grand Secretariat [Ming and Qing documents), Digital Archives for Memories and Narratives of Taiwan, among others), Taiwan Historica (including their archives of Taiwan under Japanese rule), the National Palace Museum, the National Science and Technology Museum, the National Library of Public Information, the National Taiwan Museum, and the Li-Tien-Lu Puppet Theatrical Foundation, among others. Some of the listed archives, for example National Central Library, have clickable links, so that you can get a small quick view of items such as Taiwanese stone rubbings, photographs of nineteenth-century Taiwan, and class books from the Japanese period. The Taiwan Film Digital Archives Databases also has a very nice English site, and many of the university archives are worth investigating.
National Taiwan University has numerous special collections and archives, plus a large collection of books and databases that you may wish to consult if your university has more limited resources. These include Asian American Drama, British and Irish Women’s Letters and Diaries, British Periodicals, Manuscript Women’s Letters and Diaries, and Nineteenth-Century Collections Online. See this campus map; the main library is labeled M12. For more details on using the NTU library, click here.
A useful site for government documents from Taiwan is the National Archives Administration National Development Council. The procedure for access to archives is available here. However, the archive catalog (Archives Access Service) is exclusively in Chinese.
Scholars interested in the history of Christianity in Taiwan, works by early missionaries, English mission periodicals, and the 228 Incident may wish to explore the Church Historical Archives . See also the Museum of Church History, housed in the Tainan Chang Jung Senior High School in Tainan.
Note: Some of these links change frequently. Please contact me if you come across a dead link.