I live in Seattle, so haven't stayed in any of our hotels.
In the thread CHamilton linked to, someone mentioned
the Warwick, and said it had a free shuttle. A free shuttle would be nice; I don't see it mentioned on the web site, but you can call and ask. I live a few blocks away from the Warwick and walk past it all the time and it seems like a nice place. I often notice airline crews checking in, so it can't be horrible. If you feel like a quick bite when you arrive,
Ralph's Grocery and Deli is directly across the street and is open until 2 a.m., and
the Dahlia Bakery is down the block for scones and what-not in the morning. I hear the Warwick is being renovated; if you book there, ask for a room away from the renovation, and high up -- you will get a city skyline view on one side or an unobstructed Space Needle view on the other.
I always recommend the
Mayflower Park. It's a nice older place, right downtown, and contains Oliver's, a really nice bar which is -- a little trivia here -- the first bar in the State of Washington to have windows (until the law changed back in the 1970s, passersby had to be shielded from the sight of people drinking). I can vouch for the bar; they serve an honest drink there.
The Warwick and the Mayflower Park are about two blocks apart on 4th Avenue, and the downtown Avis location is on 5th Avenue halfway between them. Which would be worth considering, if you are renting from Avis.
A friend of mine, a frequent business traveler, recently stayed at the
Hotel Andra (the old Claremont Hotel, renovated and renamed) and he liked it a lot. It is on 4th Avenue between the Warwick and the Mayflower Park. It's not inexpensive.
It is worth noting that
the Kimpton chain of hotels offers 15 percent off the best rate when you show your Amtrak ticket.
The Kimpton hotels in Seattle are the Vintage Park, the Alexis, and the Monaco. I have eaten in the restaurant at the Vintage Park (good, but probably closed by the time you get there), had drinks in the bar at the Alexis (good), and often walk past the Monaco but have never been in it.