Having visited over a half of US Capitols I can say this one is the most unusual one, and one of the most interesting.
It's located just behind the Iolani palace, which I strongly recommend visiting.
Unlike many neoclassic Capitols with the central dome all across the US, this one is a modern square building. The central inner space is open air, atrium like, while the offices and both houses are scattered around it on 5 floors.
Upon entering is an airport style security checkpoint, after which you can proceed.
I suggest first going up the top floor terrace from where you'll have great views over Honolulu. Then you can descend down via stairs and visit accessible areas depending if there's a session - we were let in the Governor's office.