The best time depends on what you are after.
If you love whales and big wave, choose January or as close to it as possible. If you want to get away from the cold, do the same. I am in Hawaii right now and have also been to Hawaii in March, April, May, September, and October. There is a difference. It is definitely a little colder and rainier in January. Although I haven't worn a jacket yet (I am the last person on earth to feel a chill I sometimes think), I have seen dozens and dozens wearing one in the middle of the day on several days of my stay, but mostly just the in the past week.
Since my favorite place is Hanalei Bay, I'll use it as an example of the ocean action. Between May and September, Hanalei Bay is as still as glass and you will see lots of sailboats anchored in the bay... a beautiful sight. If you gaze at Hanalei Bay in the winter, you will see waves big enough to draw surfers (but definitely no sailboats). Also a beautiful sight. To top it off, last week, for the first time ever, I saw a whale in Hanalei Bay. I watched it spouting periodically for at least an hour from my lanai at the Hanalei Bay Resort and have a few pictures of it, too.
There are a lot of other considerations as well, such as cost vs people watching, etc. But since my main reason for coming is getting away from the cold at home, my favorite is January and February. My current plan is 3-4 weeks within the Dec/Jan/Feb range each year. As I get older I hope to keep on adding on. And, hopefully, I'll find friends who can afford to pay their own way to come along with me!