I've spent three and a half years of my life there, and I'd take about fifteen pages to tell you all the cool stuff to do there. Rather than that, I'll give you the very truncated version.
First, this time of year, the waves will be high and the water will be colder than normal, so snorkeling may not be as fun as you'd like. There are some great places to do it, but it won't be the same as in the summer. Right now the waves are coming in, so watching the big ones crash on North Shore, especially in places like Waimea Bay, is a fun option. I've seen some that look like the ending of Point Break there. Wild stuff!
Stop in Haleiwa. It's a neat little surfer's town on the bottom edge of North Shore. Be sure to enjoy a burger at Kua Aina Burger there. One of the best in the world, and full of ambiance. The town itself is fun to poke around in, plus there are some neat beaches and trails to explore.
Be sure to visit the Pearl Harbor memorials. Get out to the U.S.S. Arizona. It's a wonderfully sobering experience, and something you shouldn't visit Oahu without doing.
Hanauma Bay is another neat experience. You can often see whales breaching just on the edges of the bay, and even if you don't, it's a cool beach experience.
If you're driving, do go around the entire island. Follow H1 west until it peters out into local roads and finally a dirt road, way out by Waianae. Take the southern loop clear around and up through Waimanalo and past Kailua, and then around the windward side until you finally go back down via North Shore. It's a long drive, but a pretty cool one with lots of little places to stop and poke around in and tons of neat hidden beaches.
Waikiki is cool and all, and gawking at all the tourists is fun, but the real neat areas are the backwoods, off-beat places--the little towns that are hardly on the map. Cruise through those and catch a plate of food at some of the little food shacks by the side of the road. Explore the back country. There are all manner of wild fruits growing wild on the island. I know places where you can pick bananas, mangoes, papayas, coconuts, star fruit, passion fruit, guavas, and probably more that escape my mind, somewhere on the island. Most of those can be found on the many hikes across the main ridge of mountains separating leeward side from windward.
In any case, have fun. And if you want to know anything more specific, just ask.
World Champion Seattle Seahawks football. It's an addiction, and there is no cure.
Les Norton - gone but never forgotten. Rest in blue and green peace, my friend.