I agree with Ol Wyo, Pearl Harbor is a must. There is a very nice breakfast buffet at Duke's Waikiki located in the Outrigger Waikiki hotel. They actually include bacon which at most other places is an expensive add-on. If you are a hiker, head up to Manoa Valley just a few miles north of downtown, there is a trail head there that leads to some nice scenery and a few waterfalls.
IMO, the island of Oahu's best attractions (besides Pearl Harbor) are outside of Honolulu. Head up the Veterans Highway thru the middle of the island to North Shore. Stop at the Dole Plantation on the way, try out the pineapple maze and have some pineapple ice cream. Stop and do some sunbathing/rock jumping/body surfing at Waimea Bay just a few miles northeast of Waialua. Stop in Wailalua and hit up Storto's for a delicious sub sandwich, a bit pricey but very worth it. On your way out of town, grab a shaved ice (with ice cream in the bottom) at Aoki's Shaved Ice. Head back to Honolulu the long way, around the island, on your way you can see the Banzai Pipeline and its impressive waves (won't be huge in October, but still not terrible). The rest of your drive around the island on the Kamehameha Highway skirts the ocean the entire way. You can turn at Kanehoe and head over the mountain to Honolulu or continue around the eastern edge of the island where you can see the island of Molokai in the distance.
Obviously there's a LOT more to do in Hawaii than all that, but just some highlights from my times there.