Free Movies on Waikiki beach – "Sunset on the Beach" hosts a 30 foot screen and shows family friendly films; food vendors and musicians perform; table and chairs set up but bring your own towel just in case; Satrudays and sundays (check times/dates: http://www.sunsetonthebeach.net)
Free Fireworks (fridays) at the Royal Hawaiian Hotel (can be viewed from the beach walk or any part of the waikiki strip)
Free live Hawaiian music in the evenings – Moana Surfrider is my favorite (outdoors under the big banyon tree; grab a drink and sit under the stars). Almost all big chain hotels (e.g. Sheraton and Marriott Waikiki good too) have live music; usually held around the hotel poolside areas.
Free Beach Walk Programs: free Cultural activities and lessons everyday (e.g. learn hawaiian chants, the hula, obake (ghost) story readings and more). ask local hotels near the beach walk for schedule.
Live Hula dancing and Hawaiian Music on the beach:
Live Hula Hawaiian entertainers (DFG—Duty Free Gallery; 8:30ish on top level). The show is to "introduce" tourists to different Hawaiian styles of dancing--Polenesian, etc. One of the few places on the island to get French crepes can be found downstairs in the food court.
Waikiki beach – jump into the ocean and take a dive! Need I say more?
Nike runs on Wednesdays at 6pm (meet at the Waikiki Nike Store next to Tiffanys/BR)