So, I used to have this awesome job. (I still have an awesome job, just a different one.) I got to type up journal entries by early missionaries from the 1850s to 1930s or so.
Anyway, in case you'd like to read some of them, here's the info on how to get there . . . :)
That link will take you there.
Alternatively, go to byu.edu. Roll your mouse over "Students," roll your mouse over "Libraries," and click "Harold B. Lee Library."
A new page will load. On the right, near the bottom, under "Unique BYU Collections," click "Digital Collections at BYU."
A new page will load with tabs. Select the tab for "Text Collections." Scroll down until you see "Mormon Missionary Diaries."
You can search by geography, diarist's name, or mission. You can also do a keyword search, like if you think your ancestor may be in one of the journals or if you know that the town you grew up in was one of the sites of early missionary work and you think maybe one of the journals would mention it. That kind of thing.
Once you've chosen a journal, a viewer will load. On the left side, you can click through the different pages of the journal and on the right you will see a scanned image of the journal page. If you have difficulty reading the journalist's handwriting, you have two options. You can scroll all the way down on the left bar and click Printing Version. Then you'll get a PDF of the typed version of the journal (without the original images). You can also change the view. This is in the left side bar as well, above the individually listed pages, next to "view." Select "page & text" and click go, and a new window will pop up with the original image, as well as the typed text from the journal.