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Flying from Honolulu, Oahu to Hilo, Big Island with Mesa Airlines for about 160 USD on May 25 with 2 day stay. The flight was only 40 minutes.
No liquid is allowed to bring in with hand luggage. Check in luggage cost 10 USD/piece.

I have stayed in Hilo overnight. I drove to Volcanoe State Parks and once around the island on also 11 and 19 which brings you back to Hilo.
I only did a 2 day trip which is of course not enough for this island.

INDEX

Akaka Falls
Hawai’i Volcanoes National Park
Hilo
Kailua-Kona
Kau Desert Trail 
Lava Tree Monument
Waterfalls