There are three main coherent nations of native Americans in the mid 19th century. They are the Iroquois Confederacy, the Red Empire and the Empire of the Sun.
The Iroquois Confederacy is a group of six nations in the north east of modern America, on the border of Canada. Their most famous members are the Mohawk nation. They are a matrilineal society, possibly also Matriarchal depending on how one defines this historically elusive concept. They have a functioning democracy and are probably the most politically sophisticated of the nations. They are bordered to the north by the Huron, with whom they are in regular conflict, and to the South by the English colonies. To their west is a disputed borderland that leads to the borders of the Red Empire. They trade and farm, and are most familiar with Europeans. An Iroquois character would speak their own nation’s language, and also would be fluent in French (the language of the Confederacy).
The Red Empire covers the area of the Great Plains, basically from somewhere around Chicago west to the rockies, and from the Canadian border down towards Texas and Florida. It is bordered by the Rockies on the west and the English colonies on the East. The Red Empire is populated by many of the Great Plains tribes, most famously the Sioux, Cheyenne, Arapaho and Pawnee. Some of these tribes are nomadic (e.g. the Sioux) and others semi-nomadic. The Cheyenne, for example, are farmers and traders, and the Pawnee live in earth houses but go on long journeys chasing the buffalo. The Red Empire is newer than the Iroquois Confederacy and less stable, with even its political structure still undecided. There are not enough people in the Empire to police its borders or its polity. This means that on the edges of the Empire there are French forts and settlements (to the North) and English forts and settlements (to the East), and on its southwest side its border with the Empire of the Sun is undetermined. It also means that the “law” of the Empire is enforced at a tribal level – although the tribes are at peace with each other and part of a common nation, they often have disputes and resolve legal disagreements according to competing legal settlements. The Red Empire is the main way by which the other native Americans, French and English can trade with each other, though, so everyone is interested in maintaining peace within the Empire, so different tribes can meet and interact and travel (relatively) freely.
The Empire of the Sun covers the conglomeration of the Hopi, Navajo Chumash and Comache people of California, New Mexico and Arizona. They are the guardians of the Grand Canyon, and another ancient and proud culture. The Navajo are the central powers of the Empire. This Empire trades with Mayans and Incas to the South, is rumoured to have a navy, and also trades with nations from across the Pacific (especially Japan, China and Russia). The Empire of the Sun is close to a religious dictatorship, however, and lacks the same freedoms and chaos of the Red Empire.
There are other tribes in America which, untouched by colonialism (or victorious against it) are thriving and powerful cultures. These three nations are the primary agents in the Compromise and Conceit One-shot that I prepared, however.