Waikiki Aquarium is the second oldest public aquarium in the U.S., founded in 1904.
People say this aquarium is smaller than anticipated and showing its age...one might say that of Honolulu itself if hailing from a larger city. It looks pretty darn good for 112, and has a lot to offer. If you're undecided, check out their website where they detail each exhibit and have a map. They have all kinds of fish and marine life - reef, deep water, predators, shark, octopus, jellyfish, corals, even rescued monk seals, and more spectacularly for Hawaii, sea horses, including some from Hawaii - but the aquarium is not just about colorful fish.
They also have, among other things, displays describing different Hawaii marine ecosystems (Kaneohe Bay, Koko Head surge zone, Kona Coast, Edge of the Reef), essential biological theory (Adaptations), tropical aquaculture, and native stream ecology. Our streams are unique, fascinating, and under-appreciated. There are shockingly few places you can go to learn about them (I actually can't think of any other place!). This aquarium may not be glitzy compared to other aquariums around the world, but watching the natural sunlight flicker across the reef is magical and they manage to pack a lot of information into the space they do have if you are willing to take the time to read the displays or listen to the audio tour.
In addition to their standard admission of $12/adult ($8 kama'aina/military, $5 seniors/children 4-12, free for children under 3), Waikiki Aquarium offers a Behind the Scenes Tour every Thursday at 3 pm, an Aquarium After Dark experience, and many other special activities and events that will entice you to visit again and again. Check out their website for more info and bookmark the Events Calender!
The Behind the Scenes Tour was a very cool experience, definitely worth the $16 admission which includes same-day access to the aquarium. You get to step on the other side of the glass and see what it takes to run the aquarium, get a guided tour of some of the exhibits, and can spend some time before or after the tour viewing the exhibits as a regular visitor.