Warning.....personal opinion here with bias openly admitted:
1) If you want to see true Alaska native (meaning indigenous peoples or "First Nations") culture, while it varies by degree, you'll only see a filtered version no matter where you go or how you visit if you do so during the tourist season.
2) FWIW, I had friends visit in 2012(?) 2013 (?) who were dead set on seeing the Alaska Native Heritage Center. When we went, in what was the final nail in the coffin of my interest in the ANHC, the staff that provided the tours was entirely summer interns from the Pacific Northwest....and they were all admittedly indigenous peoples, but not Alaska Natives.
3) If one accepts a filtered view, some of the commercial tours offered through Barrow and Kotzebue aren't bad. For a bit better view, through much more $$ and effort, I'd suggest a visit to the Pribilofs...less filtering more reality. One might consider flights to Minto, Quinhagak (Kwinhagak), Tatitlek...and any number of others that don't aren't on the typical tourist radar. It's not at all scientific, but my off-the-cuff view is that the harder it is to find lodging and restaurants at a given locale, the more likely it is to see unfiltered native culture.
