Just a few tips based on my recent visit to the Emerald City:
If you're arriving by Amtrak, you will be getting off at King Street Station, a little south of downtown. If you go straight out the door, you will be in Pioneer Square, the oldest part of Seattle. Some of this area can appear a bit rough looking, with the occasional homeless person wandering about, but it seemed safe enough to me when I was there, especially in the daytime. If you're heading uptown, you will be going uphill. I was staying at the Marriott Courtyard on 2nd Ave, which is a short walk from the station, but which has a slight upgrade, which one can notice more if hauling luggage. The cross streets connecting 2nd Ave and 3rd Ave. and so on have a more distinct grade. I don't see Downtown Seattle as hilly as parts of central San Fransisco, but the grades are pretty steep. Thus, it was a nice downhill walk from my hotel to Alaska Way along the waterfront, but a stiff climb back up.
If you are riding the Link "light rail" (more like a subway train with low, level boarding platforms), You can avoid the uphill walk to 3rd. Ave. by taking the elevator up to the 2nd floor, and then exit of the plaza facing Jackson St.. Turn right on Jackson St., cross 2nd. Ave Extended and 4th Ave, go past the old Union Station and you will soon find the entrance to the "International District/Chinatown" Link Stop. There are ticket vending machines, but no faregates. They apparently do random checks to make sure you're paying the fares. The Seattle Streetcar runs along Jackson Street and links Pioneer Square to a neighborhood called "Capitol Hill," even though Seattle isn't the capitol of anything. Note that the Link light rail also has a stop at Capitol Hill. You can buy an Orca card, which is good on pretty much everything transitwise in the city, though if you buy a day pass, I know it's not good for the Bainbridge Island Ferry, and I suspect it's not good for the Sounder commuter trains, so you would need to put some cash on the Orca card to be able to use it for those two services.
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King St. Station from the plaza on Jackson St.
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Streetcar to Capitol Hill on Jackson St.
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This is Union Station, right next to the Link light rail station, it was built for the Union Pacific and Milwaukee Road. It's no longer in use as a train station but serves as the HQ for Sound Transit.
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Here's the "Downtown Seattle Transit Tunnel," originally used for trolleybuses (or "trackless trolleys" to those of us from Philadelphia), now used exclusively for the Link light rail.
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Here's a Link train. They call it "light rail," but the parts I rode sure seemed more like metro with low platforms as far as I was concerned.
I only had a day and a half to spend in town, so I focused my visit to the waterfront, including a ferry ride to Bainbridge Island, hanging around the Pike Place Market, a visit to the Space Needle via the monorail, and a ride on the streetcar to South Lake Union.