There is a lot to do on both islands. Since you have a short amount of time I'd recommend staying on Waikiki while on Oahu so you can enjoy the beach there. You won't need a car as there are lots of restaurants in the area. I'd probably just check into a cab to get back and forth from Pearl Harbor.
For the Big Island the volcano is a must. I'd recommend staying for the evening so you can see it lit up. There are black sand beaches to the south of Hilo and to the North there are some great hikes with waterfalls.