Forgive him, to most people here Hawaii means Oahu (esp. if you're Asian) and sometimes maybe Maui.
We went to the Big Island in 2013. One thing you need to keep in mind is that it's a HUGE island. It's bigger than all the other Hawaiian Islands combined pretty much. It's also a very much laid-back "Hawaiian" feel of a place with far fewer tourists than the latter two. The scenery is amazing with tons of lava sculpted landscapes. The downside is, you will do a lot of driving if you want to see it all. It's a 3 hour drive from Kailua-Kona (where most of the resorts are) to Hilo following the southern route through Volcanoes national park.
Things to do in order along that route (Kona-Hilo):
- Kayaking/Snorkeling in Kealakekua Bay State
- Pu'uhonua O Honaunau Historic Park where Native Hawaiians used to live
- Papakōlea Green Sand Beach - this one's a bit of a hike that we didn't do as it was crazy hot out and weren't prepared
- Punalu'u Black Sand Beach
- Hawaii Volcanoes National Park (Kilauea) - make sure you see the road that was overtaken by lava.
- Mauna Kea - you can drive up to the Observatory to do some stargazing at night. Pack a jacket, it is cold up there.
- Hilo - nice little sleepy town that has a very large Japanese-American population. The mochi covered fruit store you must try. Stayed at a B&B there for a couple of nights.
On the way back on the northern route from Hilo-Kona you have:
-'Akaka Falls State Park
-Waipi'o Valley Lookout
-Waimea (cowboys in Hawaii)
-Hapuna Beach (arguably the best and most popular beach on the Island)
My advice is that you need at least a week to see the island. We had that much time and we felt kinda rushed with only 2 days on the beach.
Oh and if you have a chance try and go on a Manta Ray spotting trip. They're out of this world.