Every winter North Pacific humpback whales swim some 3,000 mi over 30 days, give or take a few, from Alaska to Hawaii. Whales arrive as early as November and sometimes stay through April, though they seem to be most populous in February and March. They come to Hawaii to breed, calve, and nurse their young.
Of course, nothing beats seeing a whale up close. During the season, any boat on the water is looking for whales; they're hard to avoid, whether the tour is labeled "whale watching" or not. Consider the whales a lucky-strike extra to any boating event that may interest you. If whales are definitely your thing, though, you can narrow down your tour boat decision by asking a few whale-related questions like whether there's a hydrophone on board, how long the captain has been running tours in Hawaii, and if anyone on the crew is a marine biologist or trained naturalist.
Several boat operators will add two-hour, afternoon whale watching tours during the season that run on the South Shore (not Napali). Operators include Blue Dolphin
HoloHolo, and Napali Explorer. Capt. Andy's now has a three-hour morning whale watch tour along the West Side. Trying one of these excursions is a good option for those who have no interest in snorkeling or sightseeing along Napali Coast, although keep in mind, the longer you're on the water, the more likely you'll be to see the humpbacks.
One of the more unique ways to, possibly, see some whales is atop a kayak. For such an encounter, try Outfitters Kauai's South Shore kayak trip. There are a few lookout spots around the island with good land-based viewing: Kilauea Lighthouse on the North Shore, the Kapaa Scenic Overlook just north of Kapaa town on the East Side, and the cliffs to the east of Keoniloa (Shipwreck) Beach on the South Shore.