Aloha from Honolulu.

I don't know you like Honolulu or not.
However, have you concerned the charge of your rent car too much? I guess that it costs only $40-50 per day for MID or FULL size car. If 2 people, only $25 per person/per day. Since you come from far from Hawaii, I recommend to spend some extra for your Rent Car, and enjoy much more in Honolulu.

You can enjoy in Honolulu or not is different issue. Many people just walk around expensive and busy Waikiki and its famous beach. Some people go up to the Diamond Head and see nice view from there. Some go to Pearl Harbor to see its musium and warship - Arizona.

There are something which you can't see at Big Island. Big Island is volcano and Lava island. You can enjoy ocean, sky and stars, mountains and golfing/
fishing. Or just simply staying the resort hotel and relax.

Honolulu is 800,000 population with a lot of high rise building, shops and restaurants. But it still has natural beauty such as Diamond Head, Hanauma Bay, Nuanu Pali.
If you come in winter, just go to north shore and see the high wave. It is really high.

If you have never been Honolulu, you might stay one night, but arrive Honolulu earlier and spend almost 2 days there.

Anyway, pleae enjoy in Hawaii!!!