I'm from Oahu so the majority of the places I'm recommending will be there but we looove Kauai!!!
OAHU
BEACHES
Sandy Beach- beach and tidepools
Portlock Spitting Caves (DO NOT JUMP)
Shark's Cove https://www.hawaiisnorkelingguide.com/sharks-cove/
Hanauma Bay
Makapu'u Beach
Diamond Head
North Shore - all of it!
SHOPPING
Town & Country surf shops
Kahala Mall
Ala Moana Mall
South Shore Market https://www.wardvillage.com/centers/south-shore-market/
FOOD
Zippy's
Rainbow Drive-in
Matsumoto Shave Ice
The Kahala Hotel Plumeria Room Bruch. See tropical fish and dolphins in their outdoor pools
HIKES
Aiea Loop Trail
Diamond Head
Koko Head
GARDENS
Koko Crater Botanical Garden
Lyon Arborretum https://manoa.hawaii.edu/lyon/
Ho'omaluhia Botanical Garden http://www.honolulu.gov/parks/hbg/
MUSEUM
Bishop Museum https://www.bishopmuseum.org/
HOTEL
Surf Jack https://surfjack.com/
KAUAI
Secret Beach
Queen's Bath (DO NOT JUMP)
Hanalei Town & beach & (small) surfing
Lazy River https://kauaibackcountry.com/
Kauai Shores Hotel https://www.kauaishoreshotel.com/
Red Dirt waterfalls https://www.onlyinyourstate.com/hawaii/red-dirt-waterfall-hi/
Waimea Canyon
Makauwahi Caves https://www.tripadvisor.com/Attraction_Review-g60615-d4521221-Reviews-Makauwahi_Cave_Reserve-Kalaheo_Kauai_Hawaii.html
Horseback riding on the beach