If you're ok with small spaces, the Seattle underground tours are really really fun.
I live in West Seattle so I'm biased, but I think the best park in the city is Lincoln park over on the west side of West Seattle. Grab some sandwiches (or ice cream) from Husky Deli in Alaska Junction then head down to Lincoln Park, get a bench down by the waterfront, and just hang out. The southern most part of Lincoln Park is the easiest way to get to the water. You can go thru the park too (which is a big beautiful urban forest) but the walk down to the water thru the park is a little steep, especially for people not used to hiking.
If dorky Americana type stuff is fun for you, there are lots of semi-pro sports happening around then. Our family likes going to the Dub Sea Fish Sticks games here in West Seattle, but there's teams all over Seattle. The Fish Sticks play low level baseball and it's much more people having a good time outside and screwing around than actual serious baseball. There's also Ballard FC for soccer, with the same vibe.
I came here to be told who to hate and instead got the tiniest bit of hope when I saw two posters with recommendations.