Flight
You can fly into SeaTac (SEA) or Boeing Payne Field, but it's easiest to fly into SeaTac. There is a light rail station at the airport that can take you into town.
Travel Note
There are loads of Airbnb and VRBO options in Seattle, as well as hotels at various price points. The wedding venue is in the Wallingford/Lake Union area, close to Gasworks Park, so if you want to stay nearby, you can use that as a landmark.
Travel Note
You shouldn't need to rent a car while you're here, though of course you can if you want! Lots of places to play tourist are accessible by light rail, and the wedding venue is centrally located in the Wallingford/Lake Union area, so Ubers and Lyfts are pretty affordable.
Train
You can get to Seattle from the airport via light rail, and you can use the light rail to get to various places around Seattle like Capitol Hill, the UW area, Greenlake/Roosevelt, or Beacon Hill. It's not as well-developed as the NYC or DC metros though, so make sure to review the station options in advance.