Cuisine in the US at that time would vary greatly based on region and season. I am from the Midwest, and when I was younger I read Giles C. Moorehad's book Historical collections of Ida County which discusses in some detail the lives of early European settlers (around 1850) in northwestern Iowa, where my family is from.

The book notes that proteins were predominantly from wild game such as white-tailed deer, elk, prairie chickens (now nearly extinct) geese, ducks and freshwater fish. Fruits were seasonal, such as wild strawberries, goose berries, currants and elderberries. Wheat and corn were common field crops and where wheat was milled into flour, corn was often made into lye hominy using wood ashes, a process similar to nixtamalization (immersing corn in an alakali solution increases nutrition and flavor). Of course, grains and tree fruits were made into beers and ciders when available. As agriculture took hold, common livestock such as sheep, cattle and hogs provided important food sources.

Perhaps someone with expertise in other regions can chime in with more information.

One of the places you can also look is in what people were eating in the various types of restaurants that existed at the time. The NYPL has a large collection of menus dating back to the 1850s. Here is their collection digitised.

http://menus.nypl.org/menus/decade/1850s

Now having looked through the menus what becomes clear is a couple of things. Firstly that a hot breakfast has basically remained unchanged. Back in 1859 you would still order bacon, eggs and some toast. The second is that food was still heavily based off English classics. A lot of roasts and vegetables. Also a great number of boiled meats and things like beef tongue. The other thing to note is just because there were not great number of immigrants some parts of their food did arrive in America in the 1850s. For example on the Parker House menu in 1859 soy sauce is on the menu as is macaroni a la Italian. Now keep in mind that these are all from restaurants and thus some of them would be not be eaten regularly even by the people who could afford to stay in them.