Sorry for my late reply as I only noticed your post tonight.
I did go to Oahu twice within same year. First time was three weeks in Honolulu, and my recent trip was for three weeks - one week in Oahu, Big Island and Maui.
Best place for sightseeing was Big Island, not much surf, but for sights (volcanoes, black sand beaches etc), and best single day was on Oahu's North Shore, watching Pipeline until the sunset.
Since you are considering flying in December, I would suggest booking early, in order to get best deals. Cheapest seats sell fastest, so start looking soon.
I booked my first trip through
www.onlinetravel.com and flew by United Airlines. It cost me £620 p.p. and had to fly to Chicago > Los Angeles > Honolulu. Took ages to get there, and would have to pay £300 if I was going to take a stopover and stay few days in LA.
Last trip was booked through
www.unitedvacations.co.uk, since I enjoyed flying with United Airlines, but more importantly I found a great bargain. By booking early (may 2003) I flew to Hawaii in December 2003 for the sum of £560 p.p. But there is more. This price included two free stopovers of my choice in the US.

So I flew direct to San Francisco (first stopover, stayed for 2 nights) > Honolulu and on my way back, route was Honolulu > San Francisco > Denver (second free stopover, stayed 2 weeks skiing) > Chicago > London.
Through United Vacations, I also purchased flights for inter-island travel, which cost me £150 p.p. and took me from Oahu > Big Island > Oahu > Maui > Oahu. Oh yes, I flew and flew and flew and...
I do not know what rules they have on taking your board with you, since I did not take mine. But I recommend you take yours, as renting one there is very expensive - much more then Cornwall.
Although public transport is awesome on Oahu and very cheap, I would still recommend you to hire a car for duration of your stay. This way, you will have no limits to where and when you want to go. But again, book early as Christmas period is busiest and cars get snapped-up fast. I left this task for when I got there, and was then told by every car rental place that they have run out of all cars. Eventually, one told me that they only had Ford Mustang Convertible for $270 per week (£150). So I took it without much complaining.
I do not know how good your surfing ability is, but if it is anything like mine, you will stay clear on North Shore in the winter

. When I did surf, I was on the Waikiki beach in Honolulu, where waves are small, but rides on the longboard are lllloooooooooooooooooooooooooonnnnnnnngggggggg!
Whatever ability you poses, you will find suitable surf.
As far as where to stay, your best bet is to look on the internet and see what sort of accommodation is available, and at what cost. I stayed at some top and not so top hotels. But if you are on the budget, get the 'Lonely Planet' travel guide to Hawaii or Oahu. I found it to be very accurate and informative, be it accommodation, general advice, places to see etc. It is one book I recommend you get.
Another place to check for user reviews is
www.tripadvisor.com. Classic site for some impartial advice on quality of accommodation throughout the world.
To book my accommodation, I used
www.virgintravelstore.com, and even made bookings for Maui and Big Island while I was in Oahu, through their site.
Hawaii is nice place and this was my first trip to the 'tropical paradise'. I was initially disappointed, as I was anticipating something different. You then realise how much hype goes into efforts to pull tourists to the destination. Spirit of Aloha has lost its meaning. Nowadays, everyone will say Aloha to you, meaning they want your dollar. Honolulu, I was told, is eleventh largest city in the USA. And on the island not more then 40 miles across. If you expect type of nightlife that you would expect in Newquay or in Europe, you won't have it. If you are into dance music, bring your own. Most radio stations play rap, with some playing rock. In December, night falls at 6pm, so nights are long, but warm

. Whole entertainment culture there seems to be centered around restaurants. I expected more cafes and bars with sitting areas outside, but not much of that kind of thing. Some way to go...
On the other hand, you will have easy access to familiar and cheap fast food, and all modern conveniences you have gotten used to. I expected food to be cheap, but it is actually more expensive then here. And my classic story of a pineapple, which is locally grown and yet costs much more then one bought at our supermarkets half a world away

.
You can probably tell that I have some mixed feelings about the place, even though I went there twice. It could be that it is really convenient to fly in winter and escape English cold. But it could also be some invisible force that is pulling me there, as I am already considering going out there again this winter. My wife would like to go somewhere else instead...