Hi JSalas,
Can give you my experience if you like.
When I went there I didn't have my Green Card yet, my passport was at Embassy having name change and I had an expired work permit.
I didn't have a DL nor a ID card.
Makes matters worse my airline ticket was in my married name, and expired work permit in my maiden name.
But airline and airport said it was ok for me to fly with expired work permit as it was a government issued ID, and if I took along my marriage license to show married name (so ticket would be ok) all will be ok.
Going to Hawaii they just wanted me to show them photo ID, both at my departure destination and at AZ where I got next plane. Arriving at Honolulu, you come off plane and you are not checked as this is classed as a domestic inbound flight.
Leaving you go through normal procedure of showing ID and so on. Security is up at Honolulu now, so make sure you pack right. Long lines leaving to, during busy hours.
I would suggest however to take any immigration related document, or copy of just in case anyone ever asked for you to prove Status.
Some States do require to prove it these days so not to get into problems, take some proof with you.
Where you going? Which Island I mean?
Kauai is my favorite.
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God Bless America - God Bless Immigrants - God Bless Poor Misguided Souls Too

Mr S.U.