If flying in, the airport is about 15 miles south of the cruise ports, which are located in downtown Seattle. The trip is a 20-30 minute ride, depending on traffic. Fortunately, there are plenty of options for reaching the port, even if you don't have a car. In general we'd recommend Uber/Lyft to the cruise port.
Where do Alaskan cruises depart from in Seattle?
The Bell Street Pier Cruise Terminal anchors an 11-acre complex along Seattle's downtown waterfront. Pier 66 is home to Norwegian Cruise Line and Oceania Cruises, which offer weekly sailings to Alaska during cruise season.