The answer is different for each whale species and where you're trying to view them from. Humpback whales are found near the Hawaiian islands to breed and give birth from November through May, with the peak time being January and February. They're spotted in the Pacific Northwest from May through September. In February, there are plenty of Gray whales in the waters near New Zealand. Blue whales pass by the Azores in April, and Sperm whales will be out near Iceland in July.