The whales spend most of their time in the Salish Sea and/or around the San Juan Islands, so naturally most of the tours leave from that area.
If you're staying in Seattle and don't have a rental car, then your best option is probably the Victoria Clipper, their boats leave from the Seattle downtown waterfront area so its a short cab ride or bus from anywhere in Seattle.
http://www.clippervacations.com/multi-package/san-juan-islands-whale-watching-sealife-search-day-trip/
There are a few tours operating out of Anacortes. The advantage of these is that you don't have to take a ferry. That saves you about $50 for the ferry ride plus saves the time of waiting for and riding the ferry each way.
If don't mind the ferry ride (or want that as part of your Seattle experience anyway), then look for boats that leave from Friday Harbor in the San Juan Islands.
There are also some boats from Bellingham and some from Victoria BC.
A few things to keep in mind:
Temperatures are cooler and winds are higher on the water, so bring a coat or sweatshirt even if mainland weather looks nice.
The boats work together to find the whales, so all the tours have a "success" rate of about 95% - which means that there's roughly a 5% chance you won't see any whales. there's also plenty of trips where you barely see whales for a few minutes - but they count those as "successful" trips.
Some tours offer a guarantee but usually it just means that if you don't see whales you get a voucher for a free trip in the future. if you're only in town for a few days, this might be worthless because these trips fill up months in advance and your schedule might not give you time for another trip anyway. Keep in mind all the boats give you the same chances, if the whales are in the area your boat will find them.
The boats are required by law to stay back something like 200 yards. Those pictures on tour websites are taken with telephoto lenses and whales rarely jump out of the water like that. Typically all you see is some water spouts in the distance as the whales surface to breath. Bring your binoculars and a camera with a good zoom if you have them.
Pay attention to the size of the boat and what kinds of accommodations they offer. For example I saw one tour that was basically a small personal yacht, limited to 6 people per sailing, outdoor seating only with no interior cabin and the bathroom was basically a small outhouse in the bow. Tours range from that all the way up to large vessels that carry several hundred people per tour with heated indoor cabins, full service bathrooms and some may even have food available on board.
Even if you choose one of the larger vessels with indoor cabins you'll get the best views from the outdoor deck areas, so bring your coat anyway.