Here are some of the best breakfast places I ate at while on the big island, in no particular order.
Basik- By far the best acai bowl I have ever had! Located in Kona, and specializing is smoothies and acai bowls. I opted for the Kilauea (acai & house-made hemp milk, topped with strawberries, papaya, granola, goji berries, bee pollen, and honey). Their products are locally grown and delicious. I ordered a small and it was pretty filling. Perfect breakfast before a morning snorkel!
The Hawaii Style Cafe- A local treasure in Waimea. Get there early because there will be a wait! I waited 30 min, but the food was worth it. The menu was stacked with delicious suggestions, and local cuisine.
Island Lava Java - A cafe located in Wiakoloa and Kona. I went to both while on the Island. The one is Kona had a much better atmosphere. They had live music and it over looked the water. However I enjoyed the food at the Wiakoloa much better. The both offer outdoor seating. I ordered the pull apart and it was amazing. It's a giant cinnamon bun filled with the cinnamon glaze. I highly recommend both the cafe and the pull apart.