I am planning a four day trip to Seattle. I would like to go on a whale watching trip on one of those days. Where would be the most convenient place to Seattle to catch a whale watching boat and possibly see some of the San Juan Islands? Thanks!

Also, where is the best place for lodging on San Juan islands

Here is a list of all the whale-watch operators in the Puget Sound Region:
http://www.nwwhalewatchers.org/members.html

There aren't too many trips that go from Seattle all the way up into the San Juans. If I were you, I would take a Washington State Ferry from Anacortes (an hour-and-a-half north of Seattle) to Friday Harbor on San Juan Island. From there, you can take a much more inexpensive (and I think more successful) whale-watching trip, and get to stay on this beautiful island as well. From personal experience, we have gone on trips with the Mosquito Fleet (Everett), and San Juan Excursions (Friday Harbor). I would highly recommend both of them.

Here is a list of accommodations on San Juan Island:
http://www.sanjuanisland.org/visitoraccommodations.html

I would recommend spending the night in Victoria and taking the whale boat from there.

Another option is taking a whalewatching cruise from Bellingham, about an hour and a half north of Seattle. I'm sorry I don't have a business name for you, was able to go with my daughter's second grade last year and we really lucked out--an orca even swam right under our boat--awesome!