Crammed into a narrow strip of land bewteen Lake Washington and Puget Sound, Seattle is the commercial center of the Pacific Northwest (at least on the USA's side of the border). With the Cascade Mountains on one side and the Olympic Mountains on the other side of Puget Sound, and Mount Rainier and other peaks visible from a number of locations, the city is certainly in a prized location.
If it is a clear day, I certainly suggest taking at least
one ferry ride, which for a fairly small price (as this is written $6.70 for single walk-on passengers going to Bremerton or Bainbridge Island and return) offers great views of Seattle and the surrounding Olympic and Cascade mountains.
There are a number of tours and tourist operators with basic Seattle tours, but one of the more unique ones is offered by
Ride the Duck, which has taken old "amphibious Duck" military craft and rebuilt them to operate in tourist service.
Another clear day activity is the
Columbia Center Sky View, which for $5 allows you to see a 180 degree view of Seattle southward, including the port, Tacoma, Mount Rainier, and the Cascades and Olympic mountains. Northward views to Mount Baker are obstructed by the offices on the north side of the building. Located on the 72 floor, the sky view is higher than the top of the Space Needle.
Though, if you don't mind climbing stairs and really want a cheap view, the
Top Deck of the Watertower inside
Volunteer Park has great views as well.
The Waterfront district is a popular tourist location, including
Pike Place Market, an aquarium, and at the far north end the
Olympic Sculpture Park and
Myrtle Edwards Park, which is the start of a bike path leading north to several neighborhoods.
Two of the large once-busy piers on the Seattle waterfront have also been turned into an entire park, known simply as they have always been known:
Piers 62 and 63. This gives the public a huge waterfront space, and at one time there were even concerts here.