Actually, that is pretty good.
Well, not knowing the times you're looking at, I can't give you much beyond what looks to be the simplest option. (I also assume that you're going to the SEA station).
The system is called Sound Transit. The step-by-step guide that I've found (with Google) goes like this:
1 - From the station, walk East on S. Jackson Street, take a right (southbound) on 5th Avenue; stop one block later, which is at S. King Street.
2 - Board 550 towards Bellevue.
3 - Get off at Main Street. (You'll be going northbound along SE Bellevue Way at this point). It looks like the stop is just after crossing Main Street, which makes sense.
4 - Walk eastbound along Main Street. You'll see a Toys R Us to your left.
5 - Turn right (southbound) on SE 112th Avenue. Google makes it look as if though you'll see a Red Lion on your left first, then the Hilton that you're looking for.
The Sound Transit website states that this will cost $2.50 per person, unless you're a senior ($1.25) or youth ($1.75). I doubt you're a senior (65+), and I'm not sure if you're a youth (6-18), either.
