Three weeks in Hawaii would be fantastic!
I've been to Oahu, the Big Island, Maui, and Kauai, and all of them had a lot to see and do. It's not all beaches.
Others have described the attractions on the Big Island, but Maui has the Road to Hana, sunrise on Haleakala, Iwao Valley, and the old whaling port of Lahaina.
Kauai has the Na Pali cliffs and a drive into the interior that takes you through several climate zones. (I also think it is the most beautiful of the islands.) You can even see the privately-owned and off-limits island of Niihau from the south coast.
Oahu has Honolulu, of course, with the Bishop Museum (of natural history and anthropology), which will teach you about what you are seeing and have seen, historical sites about the monarchy period, the best shopping, lots of reflections of the cultures of the various Asian and Pacific peoples who live there, including fine ethnic restaurants.
I've been there three times and would happily go again.