I'm taking a Research Methods in History class this semester. Essentially it guides you through writing 18-20 pages of original history over the course of 13 weeks. I don't know anything about the Old West that doesn't come from Clint Eastwood movies and Red Dead Redemption. Additionally, I've never put any thought into writing a culinary history before. With that said, I figured I would turn to the experts for some pointers on what to look for. My goal is to investigate the confluence of many different immigrant and native cultures into "Western" cooking. My instructor pointed me towards the state (Nebraska) historical archives and said that it may be fruitful to look for cookbooks, restaurant menus, and the like.
What you might be looking for are "receipts" or "receipt books". Receipts are what we now call recipes or cook books. There were plenty of them published in 1800s (in books, magazines, newspaper articles etc.), most meant for the ladies of course. But there were also a few books for cooks on chuck wagons or for cowboys on cattle drives or even for soldiers during the Civil War.
Here are a few online resources I've used:
There were, however, a lot of information about cooking included in books for the newly married woman or "magazines" for the proper lady. This included:
And I agree with your instructor about the Nebraska historical archives. I would also suggest museums or libraries in your vicinity. You could also look into cookbooks from the countries that had the most immigrants come to America at that period (Ireland, England, Scotland, Scandinavia, China, Mexico etc.) or the Native American cooking just to see how/if their peoples' recipes were intertwined with others.
Good luck!
P.S. I love Red Dead Redemption!
It sounds like you've got some great places to start. As you get a sense of what's out there, you might want to limit yourself to something more specific than "many different immigrant and native cultures." Perhaps focus on one particular immigrant group (Czechs, Germans, Scandinavians...) or on Native groups. You also might want to limit "Western" cooking to one particular area. You might even choose a particular city and research what food different restaurants and hotels offered.
Diaries are a great resource as well. A colleague of mine conducted research on her pioneer family and their food culture by looking at their diaries as well as other diaries written in the same time period and place. Often, diaries of settlers would include what they cooked, what they ate, what they (and their neighbors) raised, and what they bought in stores. If you're in or around Lincoln, you could visit the Center for Great Plains Studies and ask them if anyone is doing research on historical food/foodways.
As a starting point, you might have a look at Bacon, Beans and Galantines: Food and Foodways on the Western Mining Frontier. Again, if you're in Lincoln, they have a copy in the library on East Campus. Also, talk to research librarians. They know of area-specific sources (such as digital archives of primary sources) you can access (and if they don't know, they know how to find them).
Don't neglect newspapers. There is a big online newspaper database with OCR (scanned) issues that go WAY back that you can search for "recipes". Small town newspapers out west would be especially good.