As much as anything, Seattle is defined by its water, so a great way to experience the city is with a boat's eye view.
Assuming you haven't schlepped a yacht with you in your luggage, one of your best bets for getting out on the water is renting a kayak and venturing out on one of Seattle's many lakes. You'll find kayak rental opportunities on Lake Union, Lake Washington, Portage Bay, Elliottt Bay, and Lake Sammamish.
One of the closest to downtown Seattle (and where I rent a kayak if I want to go out and paddle) is Northwest Outdoor Center on Lake Union. It's owned by two brothers John and Herbie Meyer. You can rent single, double, and even triple kayaks there by the hour.
The shores of Lake Union (see the second aerial view of Seattle on this blog's main page) offer up plenty of interesting visuals while out for a leisurely paddle. Not least of which is the sweeping view of the Seattle skyline.
On the south side of the lake you'll find the Center for Wooden Boats and numerous waterfront restaurants. Seaplanes taxi to and from the Kenmore Air terminal here. You'll see them taking off and landing throughout the day, but seaplane traffic gets especially frequent first thing in the morning and late afternoon. I'm always watchful of them while I'm out there, but I've never had any remotely close calls. Plus, it's fun to get a close-up perspective on them in their natural element.
To the north lies Gasworks Park, where in the summertime you can people-watch sunbathers and picnickers while they people-watch you back. On both east and west sides of the lake you'll find beautiful houseboats, the least expensive of which probably costs around $500,000 (though you can head well upwards of a million if you feel like splurging).
In the early 1900's, the Lake Washington Ship Canal was dug, linking Lake Union to the Puget Sound and Lake Washington. From the north end of Lake Union, you can veer to the west along that canal, under the Fremont Bridge, as far as the Ballard Locks (or the Hiram M. Chittenden Locks, as they are officially known). Or you can head the opposite direction all the way to Lake Washington by way of the Montlake Cut if you have the time and the energy.
Besides NWOC, other places to rent kayaks in Seattle include: