Visit pike place market and surrounding area.
Ride the monorail from westlake to seattle center and back. (Optional: Then go up in the space needle)
Take a ferry ride. You can go from seattle to bainbridge island or bremerton.
Take the light rail to the UW campus and walk around.
If you like museums check out any of them.
If you like classical music the symphony, opera, and ballet are good.
If you like nightlife check out capitol hill...I guess? Not sure where the hottest night life area is these days.
If you're into tech shit maybe walk around the amazon campus in SLU.
Eat seafood and asian food. Cod Fish and chips at Ivar's on pier 54 or alternatively at the salmon house on lake union (better option imo). Put malt vinegar and pepper on the fish.
If you have a car:
Go hiking, rattlesnake ledge or little si are good casual options. Mount Si if you're more serious and in shape.
Go to any of the national parks.
Visit the San Juan islands, Whidbey Island/Deception Pass, Olympic Peninsula including Port Townsend, etc.