I haven't read the responses, so sorry if these things are repeats.
I got back 2 weeks ago - I used to go there every year growing up, now I get there every 5 years or so. I also have family that live there, so I get to find out about some non-touristy stuff. Still, nothing they tell me is as good as what's in Hawaii The Big Island Revealed - I assume someone linked that book already in here, since just about everyone there had a copy of it. It's available in the Costco there, and even some mainland Costcos.
First off, I'd swap the number of days for my own preference. Kona's beaches are a zillion times better than Hilo's. Hilo is beautiful, but fits well with a 2-day tour in my opinion.
Things I'd make sure to do:
Beaches: Hapuna (boogie boarding)
Mauna Kea (boogie boarding, great snorkeling)
Makalawena (boogie boarding, snorkeling - don't trust the guide book on the fresh water pond since the rules have changed)
Kikaua/Kuki'o (snorkeling at the north one, maybe skip without kids)
Note: A Bay is worth an hour's stroll at sunset, but not a day at the beach. You can do this on the way home from Hapuna or Mauna Kea. Similarly, Punalu'u Black Sands Beach is neat to see, but a really crappy beach to spend much time at.
Some snorkeling ideas:
Right off Ali'i drive on the Ironman swimming route - we snorkeled with the spinner dolphins there, and it was incredible.
Manta ray night dive - my wife did this and it's something she'll never forget. They're just huge and so graceful.
Kahalu'u Beach - everyone in our group said this wasn't as cool as Mauna Kea.
Mauna Kea - awesome beach plus awesome snorkeling. Very cool on the left side where there's a trench.
Beach 69 - I didn't go there, but my inlaws said it was on par with Mauna Kea.
We had kids down to 3 years old, so we didn't do any hiking. I understand there are very good hikes, but I've never done any of them - first I was a kid, then I had kids. Only one trip was between those two, and it was my honeymoon.
Some things not to miss that:
-South Point - it just feels like you're on another planet. There's so much power in the ocean there, the landscape is so extreme, the wind is so strong... just a bizarre place.
-Lava - five years ago, we were 10 feet from slowly creeping hot lava. This time, we saw nothing. The day after we went this time, though, a new vent opened, so I don't know what the status is. It's surprisingly hard to get a good update on what you should expect to see.
-Ahalanui warm pool south of Hilo. It's nothing spectacular, but feels great.
-Hilo waterfalls. Akaka, Peepee, Rainbow. I'm a sucker for waterfalls, and Peepee has the coolest forest I've ever seen on the path - I think it might all be one tree.
-Waipio Valley. I've only been down there once, and it's spectacular... but that was a long time ago and I'm not sure how hostile the locals are now. The lookout is very cool also if you're on your way around the north part of the island.
-Volcano crater. Again, we missed the floor and some walls collapsing by two days, but you have to go there just to see it.
Some other ideas:
-There's a neat drive up the hill from Kona that the book calls cloud mountain or something. It's pretty neat and short.
-Coffee plantation tour. Pretty interesting and scenic, but not spectacular. We've been to Greenwell only. Kona Joe's has a nicer building, but their coffee isn't as good (according to everyone with me - I don't drink it).
-Just try to eat a lot of catch of the day food. Along Ali'i drive, most restaurants serve catch of the day sandwiches at horrible prices ($20/sandwich), but they're some of the best sandwiches I've ever had. Kona Inn and Bubba Gump do a good job - spearfish and sailfish are nice.
-Try to take each of the roads. There's something amazing on each of them. Some south of Hilo are the prettiest I've ever seen and are marked in the guide book.
-Read the guide book. Some of the little aside comments are gold - it mentions a smoothie shack near Akaka Falls that we stopped at twice and loved. The road to get to it is also very cool. It mentions a lot of hikes that we didn't do, but might appeal to you.