As a native of Hawaii (or Kamaaina), I have been asked hundreds of times to share recommendations for MUST SEE and MUST VISIT spots on the Big Island. Here are a few of my favorite recommendations: 

• Mauna Kea summit (either on your own or with a tour company)
• Blue Hawaiian helicopter tour (if you can, the Waterfall Landing option is a life-changing event) 
• Snorkel with whales, turtles and manta rays - you can ask me where! 
• Circle the Island Tour (either on your own, or with a tour company)
• Hawaii Volcanoes National Park (coincidentally, I lived in Volcano, which is the only town in the US located within a National Park)
• Whale watching tour or cruise, or sunset sail 
• Hiking (anywhere, anytime)
• Golf the Kohala coast. If you golf, you haven't until you play here
• Waimea farmers markets 
• Hilo fish market
• Kona coffee tasting

"What can you do on the Big Island? Well, there’s golf. Fishing. Eating. Diving. Kayaking. Snorkelling. Sailing. Helicopter rides. Horseback rides. Hiking. Spelunking. Outrigger canoeing. Dancing. Fluming. Volcano watching. Stargazing. Or, of course, doing absolutely nothing."

Must-have items when traveling to Hawaii: 

A good, portable cooler:
https://www.amazon.com/Lifewit-Collapsible-Insulated-Leakproof-Portable/dp/B07QTWVMMF/?tag=rungle080d209-20

Reef-safe sunscreen. PLEASE use reef-safe sunscreen so we all have a reef to return to on future visits! 
https://www.amazon.com/Reef-Sunscreen-Moisturizing-Biodegradable-Repair/dp/B07Y9TT1K8/?tag=rungle080d209-20

Li Hing Mui powder. You'll want it as a souvenir once you get back home and crave those amazing tangy margaritas and tropical libations: 
https://www.amazon.com/Li-Hing-Mui-Powder-Umeboshi/dp/B0089PWCOK/?tag=rungle080d209-20