Although we tend to shudder when presented with the Disneyfied version of a native people's cultural history and customs, the Kiwi Haka experience is the best opportunity you'll find in Queenstown to allow some insight into the Maori way of life. An ethnic minority (about 15% of the overall population) that has seen strides taken to address a history of oppressive European behavior, you'll not get a sense of reparation from seeing the Kiwi Haka show at the theater featured at the top of the Skyline Gondola. What you will get is a further understanding of the mythology, language, and performances indicative of Maori tradition. There are four shows a night at $39 NZD per adult, while the gondola ride to the theater is $26 NZD.
Note:Any further, more contemporary sense of the Maori people near Queenstown is hard to come by in any kind of itemizable way (i.e. “hey let's go visit that Maori village!”). Most Maori in New Zealand live similarly to the rest of the population, although there are still pretty evident social and economic disparities that remain even today between the Maori and their European counterparts. If you want to experience traditional Maori living in a traveler-friendly environment, there are a number of “villages” in Rotorua on the North Island.