I know a lot about their bird collection, since Honolulu Zoo was where I got my professional break in to the zoological world!
Re the honeycreepers, they do house and (at least in the past) did breed them. While I was there they had Oahu Amakihi, and going further back they had Iiwi and Apapane and I think one or two other species as well. The issue with them is they tend to be fairly shy and easily disturbed, and are also INCREDIBLY prone to avian pox and malaria. So there were housed off display in mosquito proofed aviaries. They would be somewhat challenging to publicly display, but I suppose it would be possible.
In addition to the Nene and Io (and Amakihi if they still have them), Honolulu also houses Hawaiian Short Eared Owl, Red Footed Booby, and Barn Owl.