Transportation
Seattle finally has light rail and it has sufficiently expanded so that it's a quick and convenient way to get around. You can go from SeaTac airport to the International District, Downtown Seattle, and popular neighborhoods like Columbia City, Capitol Hill, the U District, Roosevelt (Green Lake / Ravenna) and Northgate, all the way up to the wilds of Snohomish County (Mountlake Terrace, Lynnwood). The holy grail moment of a rail connection to the Eastside (Bellevue, Redmond) will arrive in early 2026. There is also commuter rail service which is unlikely to be of any use to you unless you live a fair distance north (Everett, Mukilteo, Edmonds) or south (Tacoma, Puyallup, Kent) of Seattle.
Another very nice travel option you won't use routinely is the Washington State Ferry System. King County's Metro bus system is extensive, and Seattle is considered one of the country's most bicycle-friendly cities. The UW home page provides info on the U-Pass and other options. Those who choose to drive to campus (and really, you'll be happier if you don't) can look forward to heavy traffic and expensive parking.
Sound Transit (light rail, commuter rail) | Metro Bus Schedules
Health Sciences Shuttle (between UW & Harborview Medical Center) | Fred Hutchinson Cancer Research Center Shuttle | South Lake Union Shuttle