Waikiki
Cons: Crowded, more expensive, smells of coconut suntan lotion
Pros: You're in the middle of it all
Kahala beach
Cons: Expensive, but not as bad as Waikiki
Pros: Still in town, but a bit out of the way, you're near a golf course (if you're into that sort of thing). You're near a mall
Ko Olina lagoon resorts, specifically the Marriott.
Cons: Expensive. One way in, one way out, you need to plan a head if you want to travel, traffic out there can really suck
Pros: You're away from town, nice if you want to get away, lots of amenities. Head west and you're in Waianae (this could be a con)
North Shore, specifically Turtle Bay resort.
Cons: Expensive, you see a pattern yet? It's a bit of a drive, but hard to get lost, again the one road thing depending on route Since you're going to be here in the winter you'll be here for the big surf, traffic, one road, keep that in mind
Pros: You're away from town, near the North shore proper. Haleiwa is a nice town, part local part tourist trap, fun times!
Referral for a good Pearl Harbor tour.
Whale watching suggestions.
Talk to the hotel, in advance if possible, they can get you a good rate or point you in the right direction
Referral for half day fishing charter.
The best deals I've found was through googling. Your hotel may be able to hook you up with a group charter. Again, good to ask.
Referral for snorkeling
Hanauma bay, if you opt for the last two you're in for some driving
Which inter-island airline for island hoping or other transportation?
Hawaiian, maybe Mokulele
My wife wants to do a real luau. Is it possible to get an authentic experience?
Sorry can't help here, our definitions of luau probably differ greatly. Although I heard Germains is still ranks highly.
other
You might want to check out the Polynesian Cultural Center
https://www.polynesia.com/