The Chowhound Team split this tangent from a the Los Angeles Area board.
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I think it's possibly a cultural misnomer to speak of Native American "cuisine" in the same way we speak of Italian, German, etc. especially in conjunction with a restaurant experience. Traveling during the time before the Europeans' arrival meant being welcomed in by the local tribe and receiving their hospitality while you lodged with them. The European idea of staying at an inn and paying for your lodging and meals wasn't the cultural norm, and was likely nonexistant among the Native Americans. Even today, driving through reservation lands, you are very unlikely to see restaurants featuring Native American food, much less "cuisine." Before the coming of the Europeans, they had no metal utensils or pots to cook in, so cooking took far longer. Most of the people gathered and ate what was available seasonally. The Mono Indians around Mono Lake for example, used large sieve baskets to gather flie larvae from the lake which they dried and ate later. Acorns from the many oak trees in California provided a kind of flour after intensive preparation, and meat was usually caught or hunted, not domesticated. Excess meat was made into pemican (jerky) for traveling or later use. Most likely, the emphasis was on getting enough food, rather than raising the experience to a level of "cuisine."
"Indian Fry Bread" came into existence when the Indians who were forced onto reservations were given only minimal supplies (and often not even that) such as flour and oil or lard and had little access to fresh vegetation, etc. because they had been cut off from their normal migratory gathering routes or moved away from their cultivating areas. Despite that, "fry bread" has become a unifying cultural symbol among Native Americans. Unfortunately, this is why in some areas diabetes is rampant among Native Americans now - too much refined flour and fat and far less variety of vegetables, herbs, etc. in their diet.
There is in Native American culture the idea of the "three sisters" - corn, beans and squash - they were planted together - the beans grew and were ready first and used the emerging cornstalks as a support, corn harvested in summer, and the squash grew later and was harvested in the fall and lasted through winter. The beans helped put the nitrogen back into the soil that the corn had depleted. In this way the three kinds of food could be grown in the same square footage, requiring less area, less labor, less watering. This is why (at least on the eastern coast) "succotash" is a traditional dish that most likely originated from the Indians there.
"Authentic" Native American food cultivated, gathered, or caught and prepared in historically traditional ways is just too labor-intensive to be practical to provide in a restaurant in an on-going basis. You're probably going to have to content yourself with the Powwows Susans mentioned, or volunteer to spend a week or more at a reservation assisting with a project of some kind, or do some research and attempt to gather and cook your own. A museum or mission might be able to give you some local insight.