Aloha,
Mike & Jim - being that I'm starting training to become one of Honolulu's finest...I don't know if I should tell you where you can go really fast. Hmmm...maybe I will... :)
Actually, I've found that H-3 is a good place to get going. However, depending on your take of local superstitions it might not be the best place to go. I've gotten going pretty good on the Likelike highway as well. You can do it on H-1 and H-2 as well, you just have to know where the solo bike guys like to hideout.
Its even a struggle to find the twisties on O'ahu. There's the "winding road" leading to Waialua and Mokuleia, but that has a bad reputation as well. Then there's Tantalus drive, but there are a lot of driveways on that road. There's another drive in Kailua somewhere, can't remember the name, but it leads to Luana hills country club hidden away behind Olomana mountain. Sierra drive is good too, going up to Maunalani heights.
If you need to drag race on O'ahu, there's always Hawaii Raceway Park. $8 to get in to race from 8pm - 12am on Fridays and Saturdays. You race whatever lines up in the next lane. I once raced a Ducati Monster 900 (or whatever the cc is) in my 1500cc '67 Beetle. Now THAT's entertainment.
Street drag racing - go out to Kalani'ana'ole highway between Makapu'u and Sandy's beach. Also, Lagoon drive out by the airport runways.
If you want to chance it, you can always blast through all the two-lane cane haul roads sans streetlamps that criss-cross the pineapple fields...but...
aloha,
Joel