Yup light rail to Westlake Center station is best cheapest option.
Seattle Center area is quite large, and about a couple miles from downtown Westlake.
Depending upon what side of the Seattle Center your lodging is, you could also take the Seattle Monorail
to the SE side of the Center. Cost is $2.50 one way
But I would personally take a taxi/uber
Here are the directions from the Seattle Monorail website,
http://www.seattlemonorail.com/about/#route
To get from Sea-Tac Airport to Seattle Center, look for signs in the airport for
Sound Transit Link Light Rail. Catch the light rail from Sea-Tac Airport and get off at Westlake Center (the very last stop). From the transit tunnel at Westlake, look for signs for the Monorail, you can take the elevator (with ‘MONORAIL’ written above it) up to to the Westlake Center Monorail station located on the third floor of Westlake Center. Then, you can purchase a Monorail ticket to ride directly to Seattle Center, home of the
Space Needle,
Pacific Science Center,
KeyArena and more! Please keep in mind that the Monorail is cash only, no credit cards please.
Don't forget the EMP Experience Music Project showcase (cause it doesn't quite seem like a museum) at Seattle Center too!