Below are a few ideas but not at all comprehensive.
National Parks
Two Jewels are Hawaiʻi’ National Parks – Hawaiʻi Volcanoes and Haleakala and their websites can be easily found with a web search.
National Wildlife Refuges
https://www.fws.gov/pacificislandsrefuges/
Kauai Island:
https://www.fws.gov/refuge/kilauea_point/
https://www.fws.gov/refuge/hanalei/
Oahu Island:
https://www.fws.gov/refuge/james_campbell/
https://www.fws.gov/refuge/pearl_harbor/
https://www.fws.gov/refuge/oahu_forest/
Hawaiʻi Island: https://www.fws.gov/refuge/hakalau_forest/
Molokai (Maui NWR complex site): https://www.fws.gov/refuge/kakahaia/
NARs
See the NARs page on this website.
State Parks
A particularly interesting park is the Alakai Swamp (Kauai) which has interesting habitats and many endemic species: https://en.wikipedia.org/wiki/Alakai_Wilderness_Preserve.
Kokee state park (Kauai) is very nice for plants especially: http://www.kokee.org/index.php?kokee-flora-fauna.
Public places to see natural communities:
https://dlnr.hawaii.gov/ecosystems/nars/
https://en.wikipedia.org/wiki/Natural_Area_Reserves_System_Hawaii
Nature Conservancy reserves or places they work:
https://www.nature.org/en-us/get-involved/how-to-help/places-we-protect/?s=Hawaii