Ok, for the car question, yes, you would need to rent a car. The Hale Koa is about 11 miles from the airport. You could take a taxi, but it would cost you around $30 if not more to get there. We are going in June and rented a car for $250 for 9 days. Also to get anywhere on the island you will need a car to get around. You can take The Bus (yes that is what it is called) but you would be waiting. Just so you know, traffic on Oahu SUCKS in the morning from 0630 to about 0830 and in the afternoon from 1500ish until about 1800. Lived there for 8 years so you just get used to it.
If you want to stay at the Hale Koa, I would make the reservation soon. Don't know about the Winter time, but in the Summer, it fills up quickly. You can make your reservation a year out. We spent a little extra this time and got and ocean view for $175 per night. The price is per your rank, so the higher in rank, the higher the price. But, you are right on Waikiki Beach and a regular hotel will cost you more $$$, so it is a decent deal.
You might look into the cottages at Bellows Beach as they are on an Air Force recreation area. You can find info here
www.bellowsafs.com/lodging-rentals
. Bellows is a drive from the airport/Honolulu but you have some nice golf courses (military and civilian) in the area. You also have the MCAS Kaneohe Bay near by.
You also have the Navy and Marine Corps golf course at Pearl Harbor. There is also an NGIS on Pearl so you might look into getting a room there. Don't know the price, but it is cheaper than the Hale Koa, but you get what you pay for. If you have other question, just ask.
