For about the last 5 years, my friends and I have toured the visiting ships on Seafair weekend. We walk the approx. .3 mile strip of the Seattle waterfront (between Pier 66 and Pier 69) touring the visiting Navy ships. Last year's Seafair celebration didn't include ship tours, so we were very excited to see they were back for 2014.
We generally end up making a full day of it. We take that Friday off work, meet for breakfast, and then hit the ships. It's good clean fun, and you get to see a little of what it's like for the soldiers who have to live aboard these ships.
If you do want to tour the ships, the few things I've learned over the years are: bring, and reapply sunscreen; be prepared for long lines (the lines move as fast as they can, but there are lot of people who come to tour the ships, so be patient); and you do have to go through security with metal-detectors in order to get on to each ship so I find it easiest to travel light (keys, wallet, phone, and maybe a belt). It's also worth noting that if you intend on seeing all of ships it helps to have a vehicle to get from the ships on pier 69 to the ships on Pier 90. Pier 90 is about 2.5 miles from Pier 69. It's not necessarily a long walk (one I might make on my own, without friends in tow), but really after a long day of standing on concrete and metal, in the sun, I wouldn't recommend it.
Ship tours start at 9:30 a.m. on Thursday, July 31st. Tours go from 9:30 a.m. - 3:30 p.m. Thursday - Saturday (7/31 - 8/2), and from 12:30 p.m. - 3:30 p.m. on Sunday (8/3).
For more information checkout the Seafair Fan Guide.