Actually, Kona is a region on the big island. Kailua-kona is the town. Originally it was Kailua then kona was added to the name because the post office had a problem - there is another kailua on a different island, also hawaii. But, a lot of people call the city kona. Waikoloa is not far anyway and the poster will have a car.
There are lots of things to do on the big island. A short drive north will take you to a place that gives atv tours which i enjoyed. The volcano is a much longer drive but saddle road has been improved so most of it is ok now. They have a bike tour where you start at the top and ride down and stop by some places. Going to the waterfalls and scenic sport is fun. There is a book on visiting the big island that is really good. I never did get to the hilton village or super pool when i was there. the southern tip is ok and you can see the famous tree that grows sideways. It's actually a big tree too. Very windy there so you won't stay long. There is also the initial landing site where the first settlers arrived which is to the south also. I don't remember the names of these places but trip advisor can help you find them. Costco has cheaper gas so bring your costco card if you have one. Those precooked chickens are tasty and the costco has beer, wine, and whisky. I rented a bicycle when I was there but you may not be into that. mauna kea is good to do at least once. It's nice watching the sunset looking down at the clouds. Don't chase the donkeys.