and go there quite often and used to book tours there and checked in Japanese guests in the summers when I was at the Y.

Anyways...there is a ton to do there and you can look up the most popular.

Here are just a few that I would recommend that might be a bit off the beaten path:

Ziplines: - The best are Skyline Eco Adventure - this one is incredible as it puts you right over a waterfall (check out their website) - close to Akaka Falls, that specific line is about 56 seconds long and you'll be going almost 60mph, it's sick and recommend you get the GoPro with it. I actually took my iPhone and thought I was gonna drop it...but the view was spectacular.

The next Zipline is UmaUma - nothing close the splendor of the Skyline one, but it's close and it probably has a bit more beauty to it, and there are some great views.

If you're into stargazing the Mauna Kea stargazing thing is can be cool, if you don't want to do the "tour" thing you can actually drive up Mauna Kea and to the visitors center. Rental car agencies will probably tell you not to go, but the rode is fine especially in June.

I like to go up there during the day, try to pick a good clear day - mornings are usually better and take a jacket it gets pretty cool. The air is quite thin up there as well, so just take it easy and wouldn't recommend for those that may have health issues. A family place that was frequented often by our family paniolos (cowboys) was Lake Waiau - it's a small lake made of permafrost on Mauna Kea and you can park and hike about 1.5 miles to it. It's not a difficult hike, but because the air is thin it can wind you a bit...and can be a little hilly.

Beaches:
The best beaches are on the Kohala Coast - Hapuna is the best public beach and has pretty decent waves for body boarding. Just next door (to the north) is the Mauna Kea Hotel - now they typically give away 40 beach passes to the public - so we typically will pack a lunch and a bunch of Hawaiian Sun drinks and take a cooler and get to the Hotel before 9 am - (to insure you get a pass) the earlier the better - if you don't get one, try again around 1 pm - the Mauna Kea beach hotel is the best beach on the island - and is also great for snorkeling -because it's quite calm. You'll see turtles and Manta Rays there. I also highly recommend a sunset on that beach as well, because the sun will set at 7 pm every night and goes right into the ocean - great to see from that side of the island and from those beaches.

Turtle viewing:
The Kohala coast area has a ton of sea turtles because the Mauna Lani will rehabilitate and releases turtles almost every year, so that shoreline has a ton. What's pretty cool is that in the evenings, the turtles will come up to shore to sleep. Puako is a small community close to Hapuna Beach and there's a road just before you get to Hapuna (if you're going north from Kona) that will take you down to this community. As you drive along the main road you'll see signs of public beach access - there's really not much of a beach, but if you stop and go down one of these trails it will take you to the ocean and as the sun goes down probably closer to 7-8pm the turtles come up to shore and you can sometimes see 8-16 at one time. Just don't be a dumb tourist and put your kids on them and crap lai dat...the turtles are protected and you're not supposed to touch them at all.

Snorkeling/Scuba - Capt Cook is the place to be, very good snorkeling there and the tours are typically very good. If you're really into scuba do the Manta Ray night dive like others suggested.

Helicopter tours are some of the most expensive tours, but Big Island with the volcano and waterfalls is worth it. Blue Hawaiian Helicopters are typically the best and they have an office on the Kohala coast.

If you're a first time, definitely go check out the volcano - Especially with all the recent activity it's worth checking out - just know it's a long drive and plan on it taking a day. I recommend going north from Kona - and going around the island and down the Hamakua coast - it's beautiful especially in the morning can be the best time. I've gone a couple times in a convertible and it's amazing coastline and I enjoy stopping whenever I feel like it. On the way - stop at Tex Drive In in Honokaa and get some of the best malasadas. So good!

Shave ice -

Scandinavian Shave Ice is right in Kona on Alii drive - and has some of the best shave ice I've had (and I own a shave ice machine!).

Or if you're up towards Kohala/Waimea the Original Shave Ice Co is run by an LDS family and has some killah shave ice as well. (this is a great treat after we hit the beach in Hapuna or Mauna Kea beach - that hits the spot.

Let me know if you like to golf, there's some great courses to look at there, and also if you need some suggestions on restaurants.

Misc.
Also Kona does have a Costco, just north of Kona - and is the cheapest place to get gas so if you're going back to the airport it's on the way and I usually just fill up there whenever possible because gas is so expensive. Also great place to get souvenirs or the Walmart is also good. I usually stock up on a few cases of Hawaiian Sun first thing I do. Also, be warned, Kona around 5-6 pm can be nuts getting back into Kona and traffic can back up.

Also, my wife is a travel agent/Hawaii specialist if you need any other help or simply want a quote on some excursions. Glad to help in any way, so feel free to DM.