Others are better help on Oahu. Regarding the BI I too recommend not trying to see everything. I think you are in a great location to access a good part of the island. A lot of what you want, or are able to do depends on your interests and physical condition. My recommendations are based on my likes. I like the outdoors, beaches, snorkeling, hiking, also relaxing drinks, sunset watching etc.
That said, I second going up to Hawi and Pololu Valley hike. Drive from Hawi to Waimea, then circle back to Waikoloa. Another day drive over through Waimea, take in Waipi'o Valley. Hiking down there is much more exercise than Pololu. Then Honoka'a, down the Hamaku'a Highway, Akaka Falls and Hawaiian Tropical Botanical Gardens.
The best way to experience VNP is to stay overnight in Volcano. No timeshares there, so Airbnb or VRBO. Just double book a night. If you do that, you can finish the above drive in Volcano.
If you don't want to double book, but still want to see Volcano NP, then rise as early as you can, drive across Saddle Road to the park. Lots of very interesting things to see, short or longer hikes. Then head back over Saddle Road again to Waikoloa.
The best beaches start in North of the Airport and run up the South Kohala Coast past Waikoloa. The highway doesn't run along the shoreline, so you will need to use a beach map to find them. You said you have a convertible, so I would caution you to only go to beaches that have secure parking.
What I think you shouldn't do is be lured into driving around the island by the southern route. It has the least interesting scenery, and for part the narrowest roads. People often are urged to go that way to see "black sand beach", "green sand beach" and south point. Know that there are black sand beaches all over the island, the green sand beach requires you to leave your car unattended for several hours while you either pay for a ride will illegal businesses or walk. None of the car rental companies cover you while driving to south point or parking to go to the green sand beach. The reason is there are too many breakins. So they just disallow going to the area in total.