I have lived in Seattle since 1976 and distilling the best things to do and places to see for a less-than 24 hour visit is tough. But here goes!
First, you will be here in winter. It will get light around 7:30 AM and darkness sets in around 4:00 PM (
Sunrise and sunset times in Seattle, February 2021). The average temperature 35 degrees Fahrenheit and there is a slight chance of snow (
Does It Snow in Seattle? (When and How Often) - Sunlight Living) And of course, it rains. Seattleites don’t let the weather keep them from enjoying their city, and you shouldn’t either. BTW long-time Seattle people don’t use umbrellas; they wear hats.
Secondly, downtown Seattle north of Union Street is generally safe during the day with the exception of Third Avenue between Pike and Pine streets. I also wouldn’t be concerned about my safety walking around the South Lake Union neighborhood at night. That being said, Seattle is like any other large American city and it is always a good idea to be aware of your surroundings when out and about.
Now about sightseeing - If you want to check out the areas around King Street Station, you might delay claiming your luggage, and walk out to the two nearby neighborhoods. Go up the stairs and turn right to go to the Chinatown International District (CID) which is east of the station. The CID (
Seattle's Chinatown-International District | Seattle Chinatown-International District (seattlechinatownid.com)) seems to be making steady progress reopening from the pandemic and the summer 2020 riots. In addition to its many eating establishments and shops, the Wing Luke Museum of the Asian Pacific American Experience (
HOME - Wing Luke Museum) is the main attraction in the CID (full disclosure, I was a museum trustee until recently).
Pioneer Square is west of the station (
Pioneer Square. Seattle, WA | Pioneer Square) is also slowly reopening but is challenged by homelessness and crime. The Seattle Underground Tour (
UNDERGROUND TOUR) is the reason most people go there during the day along with the architecture although there are still several art galleries in the neighborhood.
After reclaiming your luggage and checking in at your hotel, I concur with the recommendation that you take the Argosy Harbor cruise (
Harbor Cruise of Seattle Waterfront - Elliott Bay - Skyline | Argosy Cruises). It’s a fast way to see Seattle in the context of our mountain ranges (Olympic and Cascade) and bodies of water (Elliott Bay, Lake Union and Lake Washington). The cruise ends at the Seattle waterfront. From there, walk north along the waterfront to the stairs leading to the Pike Place Public Market. The Pike Place Public Market is a complex of buildings that stretches from Alaskan Way to First Avenue and from Union Street to about Lenora Street, about six blocks in length. The Market is Seattle’s top tourist attraction, but you will be there in the off-season, so it won’t be as crowded as in summer. If you are hungry, I recommend the Athenian Café or the Sound View Café. Both places are casual, reasonably priced, and have terrific views.
Walk north about a half mile to the Olympic Sculpture Park at Broad Street and Western Avenue; there is no admission fee (
Olympic Sculpture Park (seattleartmuseum.org). In addition to the sculptures, the park has spectacular water views and a bridge spanning the north/sound railroad mainline. Walk east from the park on Broad Street about four blocks and you will find the Space Needle and Seattle Center. Seattle Center is a municipal park. The Space Needle and the nearby Museum of Pop Culture are privately owned and charge fees (
Seattle Center,
Space Needle,
MoPOP | Museum of Pop Culture in Seattle Washington).
At this point, you can walk south to Denny and catch the #8 bus back to Westlake and return to your hotel. If you still have the energy and time you could either walk north on Westlake to the South Lake Union park and take in the Museum of History and Industry (
MOHAI — Museum of History and Industry, Seattle WA). Or you could continue on the #8 and transfer to the #10 at E John and 15th Ave E. The #10 will take you to Volunteer Park where the Seattle Asian Art Museum is located.
My dinner recommendations within walking distance from your hotel include Wild Ginger McKenzie (
Seattle–McKenzie — Wild Ginger) and Cinque Terre (
Cinque Terre Ristorante (cinqueterreseattle.com)). A little farther out is Duke’s Chowder House (
Enjoy Waterfront Seattle Seafood Dining in Our South Lake Union Restaurant | Duke's Seafood (dukesseafood.com)). Duke’s is about a mile from your hotel, so you may want to take the South Lake Union Streetcar or the #70 bus.
Lastly, regarding Seattle traffic and transit, downtown traffic is much lighter now that most office workers are working from home. Metro transit buses were mostly on time even before the pandemic, so timeliness isn’t a problem. You will still want to arrive at King Street Station by at least 0915 because AMTRAK usually begins boarding 20 minutes before departure.
I hope you enjoy your visit to our city, and that the rest of your travels go smoothly.