It's tough to criticize the flag of Hawaii, but I plan to try:
As American state flags go, Hawaii's is good. There's no text, no complicated seals, and only three colors. The eight stripes represent the eight main islands. It also has a great connection to history, as it was originally flown by the Kingdom of Hawaii. It was created in the 1840's when Hawaii was a British protectorate, but modeled on both the flag of the UK and USA. The Hawaiian king, Kamehameha III, hoped to appease the Americans (there were American settlers and missionaries on the islands) while showing respect for the British Empire.
As anyone who has seen my fixes for the Canadian provincial flags will know, I'm not a big fan of using the Union Jack on the flags of non-British places (I don't really like how it's used on places that are owned by the British, but we'll get to that if I ever do a Bermuda or Falkland Islands post). In Canada it was understandable, they still maintain Queen Elizabeth II as their head of state, but the United States fought a war to not be British anymore.
One of the more admirable qualities of this flag is it's attempt to evoke the American flag but with symbolism that is unique to the islands, the number of stripes and their coloring being the most prominent. With that in mind, I offer the following as a possible replacement:
And just like that, no more United Kingdom. I can understand the criticism that the stripe colors don't really differentiate it enough from the American flag. The number of stars is appropriate, since Hawaii was the 50th state, but that could just compound the problem of confusion. My other thought was to dispose of the canton altogether, producing something like this:
This design also suggests the American flag, but does so in a way that looks less like a direct copy. The empty blue canton could symbolize the ocean that surrounds the islands and I'm prone to just leaving it empty. Someone with more artistic skill could easily fill that space with some sort of symbol of the islands (the state fish, the Humuhumunukunukuapua'a, might look snazzy up there), but I for one like the uncluttered look of the blank canton.