There is a guy his screen name is "hilomikey", he is in Hilo obviously and I think he is on the PWCtoday site.
You can ride on Oahu, but as mentioned previously, in limited areas that is until you go a certain distance offshore, then you can circle the island if you wish.
Only place near Waikiki is to go out the inlet next to what is known as the reef runway at the airport, then way out.
Other nearby option is go northeast to Kanehoe side, not far from Honolulu, where you can ride pretty much anywhere. You can also ride in Hawaii Kai area, just east of Waikiki.
Aloha.