In the Seattle area? Well, Seattle is pretty far inland so you won't see many whales besides orcas. And they're around just about all year, if you know where to look for them. Which the tour operators do. However many of the tour operators don't run tours during the winter. Probably something to do with the weather. (I live north of Seattle in a different country and we had rain on 29 of the 31 days this January.) But there's a ton of whale-watching tours, you can track them down on Google no problem.
I think there are grey whales migrating off the coast in March and April, but to see them you'd need to get a tour originating on the outer coast somewhere. It takes far too long to drive a boat from Puget Sound out to the Pacific.
It was great fun and we saw plenty of orcas. Seems there are several "resident pods" in the area (San Juan Islands, I think) and, as Paul Clapham said, the tour operators know where they're likely to be and when.
We saw plenty of orcas on our trip. A friend in Victoria we were visiting said a coworker of hers went the day before us (paying for 7 family members) and didn't see any. So it seems like it can be hit or miss.
I thought the ride on the Zodiac in choppy water was worth the ticket price, even if we hadn't seen the whales!