Any Native reservation that interests you, you'll see tweakers and run down cities but at least you'll be near a casino. I'd recommend a general "wild west" trip so you can see wilderness, ghost towns, mines and historical sites then you can hop over to a res for Indian culture. I wouldn't stay a week on a reservation unless you actually plan on volunteering in the community or seeing a specific powwow.

moundsville has a mound you can climb (with a nice view at the top)
ohio in general has some mound formations you can walk around

>>2867691
Montana has plenty of museums that have a lot of Native American stuff year-round. The actual reservations will have their pow-wow some time during the summer.

>>2867691
Powwows are a lot of fun, and they happen all over the country throughout the summer. First, think about what culture area you're most interested in. PNW, Plains, Woodlands, etc. Then find a powwow in that area that fits your schedule.

You'll get more out of it if you read about that nation's history, culture, and language, so do that beforehand. Also, if you've never been to a powwow, there are a few points of etiquette to remember that are very googleable.

File: Narragansett-Indian-Tribes-August-Meeting-Powwow-12-1350x900.jpg (346.5 KB)

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>>2867718
If you want to see New England on the side, the Narragansett Powwow in RI has always been massive and outsiders are encouraged. It's so old that the word "powwow" is literally a Narragansett loanword. Full disclaimer that their rez is tiny (a few square miles) but tribes from all over the Northeast come up for it