Welcome to the forum.
I lived on Oahu back in 2006/2007. About the only easily accessible caves I know of on Oahu are near Kaena Point in the west.
Kaneana Cave is right by the road, and although not very extensive it is probably the most well-known. If you decide to do the Keana Point coastal hike at the end of the road, take a headlamp as there's another small cave right on the trail near the point. You can't miss it. The nearby albatross colony is pretty cool too, and you may see some whales and sea lions.
The Big Island is a different story, and as you may know it contains many of the longest and deepest lava tube systems in the world. One little easily accessible public cave is right by the road at
Kaumana Cave State Park. It would also be well worth your time to visit the southern part of the island, and go to
Kula Kai Caverns. Not just a small "tourist" cave operation, this is also a major hub for project caving on Hawaii and the home of the
Cave Conservancy of Hawaii.
Hope this helps. Good luck.