The only charge for Diamond Head is to park and that was about $5. The Arizona Memorial at Pearl Harbor is free, but they have timed entry. If you want to see the USS Bowfin, USS MIssouri or Pacific Aviation Museum you have to pay.
There really isn't much to do at the Dole Plantation. I booked the PCC excursion through Aulani and we stopped there for about 30 minutes. I was glad I hadn't set aside a separate time to see it. We also went past the north shore on our way to the Polynesian Cultural Center(PCC), so I didn't feel like I had missed anything by not making a special trip to see it.
If you like museums, the Bishop Museum and Honolulu Academy of Arts give you a great overview( especially the Bishop Museum).
There are a lot of things to do at the resort: crafts, tours, kayaking, etc. I believe there is a copy of the daily Iwa somewhere online which is the daily Aulani activity guide. There is also the Paradise Cove Luau which is next door at another resort.
Happy planning!