Since I live here, I have not stayed in a hotel here. So, I can't tell you about the rooms and customer service all that. But I can talk about locations, and I will say, I wouldn't stay at a hotel south of the station, because you would be that much farther from downtown and the various attractions. So, the Silver Cloud Stadium would not be on my list, for that reason. On the other hand, you could walk up the block east and look at trains, so there's that. And it's a brand-new hotel, maybe two years old.
Also, I would not stay in Pioneer Square, just because the bum-to-normal-person ration is too high there. I go there, I shop there, I eat there, but I wouldn't recommend staying there to a visitor.
The Arctic Club Hotel, referenced above, is a new remodel of a historic old building, and is relatively close to the station (0.3 miles, says Google maps), totally walkable if you have a wheeled suitcase or light luggage.
Two hotels that you might consider are
the Mayflower Park and
the Warwick. Both are on 4th Avenue towards the north end of downtown, and if you are willing to tote your luggage from King Street Station over to the bus stop on 4th Avenue next to Union Station, a distance of about two blocks, you can get to them for free on a city bus. As I said, I have not stayed in them, but I walk past them all the time, and sometimes drink in the bar at the Mayflower Park, and they seem nice, with the Mayflower Park perhaps the nicer of the two. I just looked and both have rooms for under $150.
If you wanted to try something a little cheaper than those two, there is
the Ramada, which is near the Warwick, and looks well-maintained from the outside. If you want to watch the monorail go by, ask for a room on the 5th Avenue side; if you don't want a (fairly quiet) train going past your window all day, ask for a room on the Blanchard Street side.
He got a nice reward.
