"Field Notes from the Russian Front" by Stanley Washburn would be worth looking into. He was an American correspondent covering the Russian campaign for the Times. It only covers the early stages of the war, being published in 1915, but provides a pretty solid eyewitness account through the early winter (although as with any eyewitness, take it all with a grain of salt and try to verse yourself in more objective accounts of events to compare with). And most important for you, that means it is 100 years old and available for free online!