We've spent a week in Kona on the Big Island about 8 times with family.
1) Don't drive around the island in a day, unless you like that kind of thing. It seems like work to me. We stayed at a B&B in Hilo a few times and we recommend it highly. It is a great place to break up an island circuit.
https://www.halekaihawaii.com/rooms
We liked the Bamboo room the best. The sun comes up out of the sea out that window.
One morning we hear all sorts of laughter and loud talk, and found out that the locals would surf right below us to the right when the waves and tide are right
2) The cross island highway is a good one day over and back if you are based out of the Kona area. You can go to the visitor information station partway up the mountain, we enjoyed that. Beware of high altitude, if you are sensitive to that.
The saddle road tops out at 6765 MSL, and the Onizuka Vistor's Information Station is at 9300 MSL.
https://goo.gl/maps/YzrVtE1KwULFcryZ6
3) Do allow some time for the Kohala. It is mountainous and spectacular.
At the end of the road you find the Pololū Valley Lookout. Before you head back, take a look at the Kēōkea Beach Park. It was nice, big waves to watch and just a chill little park.
4) We enjoyed Waipio Valley. We've done wagon rides, rode ATV's on a trail above to the overlooks, and just enjoyed the history and tragedy of the area. It was devastated by the 1946 tsunami.
Now the valley is closed to all but locals due to slippage and failure of the road down into the valley, but you can still see the overlook.
There is much more to look at so ask away.