I would guess that nearly all of the counties in the United States have a local historical society. A Google search on the terms "historical society county state" shows millions of results. If I choose a county at random, such as Kane County, Utah, the first thing I discover is how many states have counties with the same names. The next thing you will discover is that you might have to be creative to find the equivalent organization. There may be a museum, library or even a city office that handles the "historical" documents of the area. For example, the Google Search for a Kane County, Utah Historical Society, did not show any results, but it didn't take more than a minute to find the Orderville, Kane County, Daughters of the Utah Pioneers Museum. Of course, Utah has a State Historical Society and has over 65,000 images online. In Utah, the State Historical Society and other organizations are part of the Utah Division of State History. Other large and established organization include the Daughters of the Utah Pioneers with a very substantial museum up the hill from the Family History Library in Salt Lake City, Utah. Utah is in no way unique in this regard. With a little bit of searching, you will find similar organizations and collections of historical and genealogical documents scattered across the country.
One thing you will also find in abundance is a number of "old timers" who are willing to talk about the early history of almost any area. I once stopped off at the library in Seligman, Arizona and in a few minutes the librarian was on the telephone trying to put me in contact with some of the "old timers." Sometimes, all you have to do is ask.
Another interesting and helpful resource is the local mining, railroad or whatever museum. There is even a Moonshine Museum at the Hillcrest Orchads in Georgia. Some of these "museums" are maintained by commercial enterprises, such as the Dole Pineapple Plantation that I visited recently in Oahu, Hawaii. Never underestimate the amount of genealogical information contained in the files of these "museums." Check out the entries for each state in the FamilySearch Research Wiki. Most of the state articles have an entry for societies.
Many of these museums and societies are underfunded and understaffed. They may only be open by appointment or on very limited days. It pays to do some homework and get on the telephone or computer and talk to the society before attempting to visit. Some of the state historical societies have a list of all of their local historical societies. The website for the State Historical Society of Missouri maintains such a list entitled the "Directory of Local Historical Societies, Museums, & Genealogical Societies in Missouri." Such organizations may appreciate a donation or gift. In one county historical society, I was told that they "did not allow photographs of their documents." After a few minutes discussion, what we determined was the issue was that they made a substantial amount of their operating expenses by charging for photocopies. I got permission to photograph anything I wanted, by simply paying the equivalent copy cost for each photo. They were happy and I was happy without the paper.
So where would an historical document or photograph end up? Well, the answer to that question is "just about anywhere." But it pays to look in places where the people involved have an interest in maintaining such old documents and photos.