@JLeslie I don’t know the current situation, but in the past there has been a fairly regular ferry available from the San Juan Islands to Victoria.
The other suggestions are good and I don’t know what to add not really knowing @janbb.
I agree that the top of the Space Needle makes great sense (iconic, spectacular, shows you everything, near to downtown and the Seattle Center). And the Pike Place Market is of course also iconic, different, downtown, great to walk around and explore, atmospheric, etc. They both give a good flavor for old Seattle (which IMO is the best flavor of Seattle).
If you start out by going to the Space Needle roof so you see the layout of the city from the air, then you can take the Monorail (!!) which is next to the Space Needle to downtown and you’ll be just a few blocks from the Pike Place Market.
Other ideas if you have time:
The Space Needle is also inside the Seattle Center (expo park from the World’s Fair when the Needle was built), which has other attractions that might or might not appeal: The Science Center (hand-on science and traveling exhibits, the Sci Fi museum, Experience Music Project, iMAX theater, Laserium, etc).
The Pike Place Market is just uphill (Seattle has hills) from the Seattle Aquarium, which is a nice if-not-spectacular/large aquarium with cute otters & seals and octopus, hands-on starfish, a cool underwater observation section, and an iMAX theater that probably still shows short iMAX films of Mt St Helens blowing sky high in 1980.
The downtown Seattle Public Library is quite spectacular and interesting. It’s more like a Tomorrowland exhibit than a library, while still having books.
There are some theatres, opera, concert hall and ballet if you’re into that. The 5th Avenue Theater is fairly spectacular inside.