The Contemporary Museum (TCM) in Honolulu is...contemporary (read: weird) so most people won't like this place. However, it's air conditioned and near Punchbowl Cemetery. So if you visited Punchbowl and have extra time in the afternoon, want to cool off, have lunch, and pick up a few gifts, then it's worth it.
Or you can do what those people are doing and just chill out on the lawn.
The two things that I liked about TCM was the gift shop and the Contemporary Cafe. The gift shop is small, but is packed with several humorous and local items. One item that stood out was the T-shirt above. As for the Contemporary Cafe, the one thing they do that other museums don't is make you a box lunch. But, you need to call ahead. The Cafe is lined with various art however, I wasn't able to try the food because the Cafe was closed. So maybe next time.