Not sure if you're into art, but visit the
San Francisco Museum Of Modern Art. Strong permanent collection, and if anything, the interior architecture is impressive. Just try NOT to feel giddy when you're walking that steel platform several stories high above the atrium. The museum itself is on the edge going into the SOMA (South of Market), the S.F. equivalent of SoHo in New York - lots of overpriced art galleries and pouffy places to shop and eat.
Best place to feel spooked is
Fort Point, right under the Golden Gate bridge. It was built over 100 years ago in defense of the city from sea attacks. It FEELS like you're in an adventure game exploring some haunted place for clues. I've felt some weird presences there when I poked around the bunkers on my own. Pretty cool.