These are good questions to ask the outfitter. (I can't recommend one there, since I've only rented kayaks in Seattle for San Juan trips, and the business required that you had taken one of their classes, and they also required that the renter have kayak racks on their vehicle.)
You don't say what your skill level is, but it's really important to communicate this to the outfitter, who can then suggest a route. There are some tricky, nasty passages in the San Juans-even motorized boats avoid certain places.

That said, if you want to see whales, your best bet is the west side of San Juan Island. Not too many places rent kayaks by the day without a guide, so in terms of what harbor to start from, I imagine you'll be somewhat limited by where they are willing to drop the kayak.

There is a book that might be helpful called "Kayaking Puget Sound, the San Juans and the Gulf Islands."

thanks Christy...we've kayaked and canoed the rivers around here forever and took a sea kayak out for a spin while in Mexico a couple of years ago. We've owned boats and/or jet-skis for years as well so we are not strangers to the water. I guess the real question in my mind is where to launch...Friday Harbor and Roche Harbor seem to be the main ones. But sometimes the main ones aren't the best places...just the best advertised. That's why I wanted info from people who have been there.