The Palau International Coral Reef Center, on the road between Koror and Malakal, is part aquarium and part working research institute. The public exhibits are arranged by habitat — mangrove, lagoon, outer reef, deep water — so you can see in tanks what you are about to see on the reef itself, often with a card explaining how each ecosystem connects to the next.
The centre also runs Palau's marine research program and is involved in the management of the Rock Islands and the country's huge marine sanctuary. Go in the morning before a boat trip and the day's diving will make more sense.