You are under 21 and yet you want a drink. This contradiction has only one legal solution: cross the border into Canada, where, in British Columbia, the legal drinking age is 19.
One advantage of going to college in Seattle is that you now live close to a saner country—a place with national health care and the good sense to stay out of Iraq and a sensible drinking age. You are also blessed by the size of Vancouver, BC—it's not just a city in a sane country but a big city in a sane country. And like all big cities, it has lots of bars filled with other young people to meet and fuck.
Vancouver also has lots of cheap but decent hotels. My recommendation: the Shaughnessy Village in Vancouver's hospital district. This concrete tower offers small but cozy rooms that can hold three persons at the cost of fifty bucks a night. If you decide to stay here, ask for a room on an upper floor facing downtown Vancouver. For fifty bucks you will enjoy a million-dollar view. As you legally drink and fool around with your friend (or friends), the lights of the city will magically illuminate your lurid little room.
Another advantage of Vancouver—that it is only three hours away—is undone by a major disadvantage: From around 9:00 a.m. to 9:00 p.m., the border is practically impenetrable. The lines to the border check are longer than the Great Wall of China, and nothing, not even the hardest of drugs, can speed the never-ending wait. (I recommend taking the train on Saturday morning and returning on Sunday night—the train takes about four hours, is comfortable, and has bathrooms with just enough room for rocky sex.)
Another disadvantage just now is the weakness of the American dollar. Canadian prices are inflated by taxes that help support this sane country's social services, which makes drinking bloody expensive. And while the Canadians enjoy a generous health-care system, they do not enjoy generous pours. But a weak Canadian drink is better than no American drink.