I live here...
In January, swimming is doable all over the island - but watch for big-surf if you go anywhere that is not protected by a sea-wall or reef. Ala Moana IS the warmer place to swim especially when the sun is shining as the water is shallower and warms up quicker, plus the swimming area is sheltered from cooler water by the reef/rock wall protecting the inner area. General rule of thumb for water temperatures here - if the land is cool, the water is warm. If the land is warm, the water is cool.
Time will be a major issue. Since you are traveling internationally, you will have to get through immigration and customs just to get out of the airport - THEN on your return spend another 2 - 3 hours just to get back past TSA & customs to catch your flight! Especially if you are going through in the evening hours - there are more evening flights OUT of Honolulu and you will be in lines with lots of other people. When crowded, TSA can take upwards of 1 hour alone.
So guestimating you will have about 6 - 8 hours total time to play around on the island (being conservative here).
I STRONGLY recommend taking a bus ($2 USD one way) to Downtown Honolulu. There are so many attractions there and you will not be too far for a cab ride if you run short on time. Actually, you can take a cab to the Aloha Tower Marketplace, walk the downtown/Chinatown area, then get back to the Aloha Tower for a cab back to the airport (easiest - but not necessarily the cheapest).
In the downtown area, you have the following:
-->Chinatown (great shops with quality imports and some touristy items)
-->Bishop Square (@ lunch time something usually happens here, either live performance or something)
-->Iolani Palace (daily tours during the week, sometimes will have the Royal Hawaiian Band playing in the bandstand for lunch hour if the weather is agreeable)
-->Capital District (historic buildings and some statues that touch on Hawaiian history - including the world famous King Kamehameha statue)
-->Missionary Houses (great museum to visit and learning experience w/tours)
-->link with more information:
Aloha-Hawaii.com: Exploring Downtown Honolulu
If you go to Ala Moana center you can enjoy the shopping, then go across Ala Moana Blvd. to Ala Moana Beach Park. You can do this inexpensively by catching any bus from the airport to Ala Moana (it is the end of the line generally). Catch some rays, eat a plate lunch, then get back to Ala Moana Blvd. for the bus back to the Airport.
Going to Waikiki is okay, but in 6 - 8 hours you won't get much time to take it all in. The Royal Hawaiian Shopping Center is nice for shopping, but more expensive than Ala Moana.
Even if you take snapshots of things, you STILL will not get to enjoy it all.
Arizona Memorial... IF you go to the memorial, that will be your entire layover. If you do not get there early (7 - 8am), you will be in a loooong line which will eat up most of your precious time - the tour buses start arriving at about 7:30am. Then you sit through the presentation (about 45 mins) and then again in a line for the ferry to the actual memorial... if the harbor is not choppy. In January, it may be choppy... so best not to stress yourself by chancing it and then missing out on some good beach time or touring the downtown area - both of which are VERY memorable and fun "day visits".
I've had friends from Australia layover here for that amount of time. I took time off from work to drive them around and it was enjoyable, but MUCH too short to do any serious site-seeing. Even going to the Pali Lookout was harsh as we hit it about 3pm - the beginning of pau hana traffic (what we call rush hours here - yes.. hourS).
If you want to go to the Pali Lookout, or anything "out of the way" (and in this I mean the Arizona Memorial), then you will want to rent a car.
Car rentals here are not cheap... nor are Taxis. The best value you will get will be to Ala Moana, or Chinatown and the Historical District around the capital.