Keep an eye out at Kekaulike Market — you're likely to uncover some treasure or funny trinket among the stalls here. After you've had a thorough browse of things, try some fare from one of the local food vendors.
You'll find this community marketplace in Downtown Honolulu. Once you've seen all you can at Kekaulike Market, consider visiting nearby Diamond Head, University of Hawaii at Manoa, and USS Arizona Memorial.