My son and I did three days of bike touring in the San Juan Islands last year, and it's definitely do-able to pick an island to stay on and then take the ferry "out" to your riding destination of the day.
We chose to stay in Friday Harbor because there were several lodging options right by the ferry, and we wanted to be able to get to and from the ferry quickly. I think if you stayed on some of the other islands you're likely to have a bit of a haul to get to the boat each day.
I think if I had to do it over again I would do it in 2 sections:
1. Stay on Lopez Island the first day, and do the loop of Lopez Island.
2. Second day, take the ferry to San Juan Island, and do a lap around San Juan Island.
3. Third day, move my base of operations to Orcas Island. Then take a ride.
4. Day 4, Ride to the top of Mt. Constitution. Tough climb, beautiful view, totally worth it.
5. Day 5 - poke around Orcas some more, or take a day off the bike.
The roads are all chip seal but -- based on my experience -- not as bad as Texas!