To get to a destination, the best way is knowing someone who lives in the city! If not, there's also different commuting methods to try out. I've gone to Seattle in a number of ways and here's a few:
1. Casino Bus: This is probably the least expensive, but also the most limiting way. With a small fee (<$10), they take you from Vancouver to Seattle. There's a number of casinos in Seattle that provides this service. Though its a half-day trip, it is a much cheaper alternative if you are looking into a day outta town without paying too much for gas. If you're lucky, you can visit the stores nearby after putting in some $$ in the casino. The Tulalip Casino is situated beside the Seattle premium outlets so shopping is about a 5 minute walk away.
Good for: Half-day outta town
2. AmTrak: The most expensive, yet the most comforting method! The train is rarely full (except the memorial weekend) so you can pretty much choose to sit elsewhere with an extra seat to put your belongings. They have comfy leather seats with power outlets for your electronic devices. There is a small lounge if you want to get some food/alcohol beverages. Wifi is available on the entire trip, connection is strong enough to run flash games. Going past the border is really convenient as you've gone through the inspection before you head on the train. So the border officers come on the train & asks a few simple questions. The pitfall is that the train has more stops than buses so it will take about 2-3 hours longer than a bus to get to Seattle. It is roughly $54 one way & runs twice per day.
Good for: >1 week vacation
3. Boltbus: This is the second least expensive for a weekend getaway. If you're looking to take a break & head outta town but don't want to drive, this is your best alternative. Boltbus is run by Greyhound company & offers a cheaper alternative for passengers going back and forth from Seattle/Portland from Vancouver. Their bus stops are located beside the train stations so getting to places from arriving is not a problem. Wifi is available half way (in the US). They have leather seats and the bus is usually full going to Seattle & less people coming back to Vancouver. There is a young crowd for this service & bus drivers are really helpful/knowledgable. It is roughly $19 per way.
Good for: weekend/outta town short trips
The above is all personal opinion & is not sponsor/affiliated in any way with those companies.