Most things I've read have said that it is whale season in Hawaii from November through March, with some whales coming sooner and some staying later. We didn't start really seeing them until January, with February being the best month for whale watching so far .
If you're going to be here for a short time, and want to see whales, I'd recommend coming in January and February. It might be worth your while to go on a whale-watching tour boat, because you're pretty much guaranteed to see whales that way. If there are more than just two of you, you could for the same money, arrange for a private fishing charter to take you whale watching instead. You could save money, and have less people standing between you and the whale.
If you really want to save money or see the whale again, then you can see whales from the shore line. Even when the whales are close to shore binoculars make the experience better. Binoculars that you don't have to worry about getting wet or splashed with salt water are the best. The same goes for your camera. Still, I think being on a boat gives you a better chance of seeing the whales.
Bill's been on four whale-watching boat tours. The one he took in Maine is still his favorite, because the whales came alongside the boat. He did two from California, one only saw a whale twice at a great distance, and one we didn't see whales at all but we were on a inflatable Zodiac boat which was fun, as we easily saw over 1000 dolphins, which was fantastic.
One day the four whales traveled back and forth at the mouth of the bay at sunset.
One day a mom and baby came into the bay and swam really close to the shore and the snorkelers that were in the bay.
People have said that the northwest coast of Hawaii is even better for seeing whales. Our tour was actually supposed to start further north, but because of high winds and waves, we were taken to the Kona Bay instead.
When we've been on the northwest side of the island, we've been able to pull over at the roadside overlooks and watch whales. Nice, but not as impressive as being close enough to hear them blow.
In fact when they are close, the sound of their spout will alert you where to look.
I can't write about whales without mentioning numbers. At one point it was estimated that there were 1,500,000 humpback whales in the ocean. When they were declared an endangered species in 1964, it was estimated that only 1000 humpbacks were left in the whole world. It has taken them almost 49 years for their numbers to grow to around 80,000 individuals. Around 10,000 of them visit Hawaii every year to give birth where it is warm and breed. It has been said that one million people visit the islands to see them.