Recommendations for must do activities Kauai and Big Island

This reddit thread has been full of great (and overwhelming) information for our upcoming first ever trip to Hawaii. I have lots of ideas but no firm itinerary yet and wanted to hear your must do/see. In Nov we are in Kauai for 5 days and on to BI for 6. We are an active 65 y o couple, love nature, hikes, history and unique experiences.

We are not resort/condo people and are looking for accommodations that support and reflect the local culture. We have reservations but we can cancel till the end of Oct so if you have someplace you love, please let us know.

TIA !