The spring powwow is at Mather Park. A few years ago, the Menominee Social Club of Chicago (the first recognized off-reservation body of the Menominee nation) built an "Indian Village" in Welles Park.
The American Indian Center (do a google search with AND Chicago) puts on the big powwow that is end of season. They are the largest urban Indian center in the country, dating back to 1954 I think. They have a good website that has a powwow calendar.
Many powwows have themes, like honoring our veterans, sobriety, youth, etc. They are all different and interesting in their own ways. Many are out in forest preserves, etc., are relatively small, good places to take kids, and you can see some things like naming ceremonies and give-aways.
For David Hammond, consider wearing the t-shirt an act of supporting the vendor. If you can express solidarity through what you eat, why not through what you wear? My husband wears one that says The original gangstas and has pictures of Geronimo, Sitting Bull, Crazy Horse, and Chief Joseph. It always gets comments and raises awareness (reducing invisibility). Especially important around Thanksgiving, don't you know (also Columbus Day, no offense to Italian-Americans, but it considered almost a day of mourning among Native Americans).
Was there no corn soup at the powwow? It's a typical woodland tribes offering, but it often sells out early.
My favorite description of what are in the southwest called Navaho tacos came from my Italian brother-in-law, the chef, who ran three hospital kitchens, including cafeterias open to the general public many years ago. I was planning a visit to the Denver Botanic Gardens while visiting one day, and he suggested I stop by for lunch, and mentioned that they were serving Navaho Tacos, which were wildly popular. I hadn't heard of them, and when I asked for an explanation, he said "they're basically pizza frite."