mt rainier, mt st. helens, pike place, EMP, Fremont troll, sports game, Alki Beach (best view of the city as a whole), go get some Dicks on Queen Anne, go see a show at the Showbox, umm there is alot of stuff. depends on how much time you got and what you like to do and how much time your going to have available!
Anyone coming to Seattle must drive northbound 99 on the Viaduct. Best views of the town and water are from the Viaduct. Go to Alki Beach in West Seattle, rain or shine. Go to 1st Starbucks store in the Pike Place Market. Ride the Monirail to Seattle Center and at a minimum look at the giagantic bolts that hold the Space needle down. The 46th floor of the Columbia Tower has a Starbucks and a view of Mount Rainier to die for. The UW campus is awesome and big, walk the Mountlake Cut trail, go to U-Village, rent a canoe or kayak at the Hec Ed - Lake Washington side see if the Observatory is open. All on or near the campus. Comedy is fantastic in Seattle, go to Comedy Underground or Giggles.