As Garyloo said...its cruise season.
Also June is the start of numerous summer events/conventions in the city.
This year one weekend in June is commencementat the Univ of Washington is june 13.
the following weekend the US Open golf turnament is happening at Chambers Bay just south of Tacoma. They have talked about running an express SOunder train from King St Station (downtown/stadium) to the golf course (with posisbly one stop near the airport) that will bring people to/from the tournament.
the first weekend of June is the last weekend of the Seattle Film festival (starts in mid May)
http://www.events12.com/seattle/june/
look outside of the immediate downtown core. Generally cruise Passengers are going to stay in the downtown area near the piers within close walking distance.
Look at the airport hotels. there are two light rail stations. One is at the airport and the other is juts north of the airport on the edge of the airport hotel district. There is a comfort inn right across the street from the light rail station so you could use that to get i nto the downtown core.
Another option is staying in the subrubs and commuting into the city.
At Seattle convention center in downtwon:
6/4-6/7 conventon expected 1,000 people--AADSM anuual meeting
6/14-6/17 convention expected 3,500 people--ASEE annual meeting
6/19-20 convention expected 10,000 people--Seattle Pet Expos
6/24-28 convention expected 6,500 people--AOA Annual Optemtry meeting