Here's the perspective of someone who's lived his whole life in LA and never been to Chicago.
Chicago
I think I only recognize the Sears/Willis Tower in establishing shots of Chicago. If it didn't have it's antennae, I don't know if it's truly distinctive or good looking. It does have a cool "evil" look, however. The John Hancock Center superficially looks too much like the Sears to quickly ID it in brief establishment shots. It's exoskeleton is beautiful and iconic, however. I laughed when I heard Smurfit-Stone Building (aka Crain Communications Building) but I've definitely seen it before. I love the architecture but I wouldn't necessarily associate it with Chicago. Another building that I didn't know was in Chicago is the stunning Marina City, probably known as the the cover subject of Wilco's
Yankee Hotel Foxtrot.
The University of Chicago is world famous but I'd never recognize it from a photo; ditto for the Art Institute of Chicago.
The Field Museum and Shedd Aquarium, I know are famous, but I couldn't place them in Chicago.
I really didn't know about the Adler Planetarium (looks nice) or Navy Pier until going through this thread.
Cloud Gate is something I've definitely seen but didn't associate with Chicago (notice a pattern)? With more repetition, it's a shoe-in to become an instantly recognizable Chicago landmark.
In summary, Chicago has many worthy landmarks but to someone who's never spent time outside of the west coast, Chicago, Detroit, Boston, Philadelphia, etc. tend to get blurred and absorbed into the overwhelming media shadow of New York.
Los Angeles
I guess it's undeniable that the Hollywood sign is recognizable within a nanosecond. Do people outside of SoCal know that Hollywood is a neighborhood of Los Angeles? I have to admit, I'm a little embarrassed that an advertising sign has become the most famous landmark of LA, even though it does have an interesting history. On the other hand, it's simple and direct, unlike a skyscraper that might take a moment to recognize.
As far as LA skyscrapers, the U.S. Bank/Library/First Interstate Tower is probably the most famous. Its greenish white hue and crown are pretty recognizable:
U.S. Bank Tower
The Frank Gehry designed
Walt Disney Concert Hall has become an LA landmark. It would have been even more iconic if dawdling hadn't delayed its construction until the Guggenheim at Bilbao was finished. Everyone thinks that the Disney is a copy of the Guggenheim when it's the other way around.
Grauman's Chinese Theater and the handprints are well known Hollywood landmarks as is the Hollywood Walk of Fame.
The Hollywood Bowl, nestled in the Hollywood Hills is often seen in photos.
Santa Monica is an independent city which is completely enveloped by LA, and the entrance to the
Santa Monica Pier is pretty famous.
I think the 2nd Street tunnel in Downtown LA, between Figueroa Ave. and Hill St. is widely seen in movies and advertisements but most people probably don't know that it's in LA and Angelenos probably don't know where it is in the ctiy. The western opening at Figueroa is particularly distinctive with its fluted detail as is its glossy white interior:
2nd Street tunnel, DTLA - Wikipedia
Chris Burden's
Urban Light, an outdoor installation on the Wilshire Blvd. entrance to the LA County Museum of Art has a chance of becoming an LA icon--distinctive and easily captured in a photo.
Venice Beach, which is in LA proper has a few landmarks. The boardwalk with its eccentrics and Muscle Beach are well known but hard to capture in a photo. On the other hand, there is the
Jim Morrison mural and the Frank Gehry designed
Binoculars Building (now occupied by Google).
My personal preference for LA landmarks would include
Los Angeles City Hall since it's been on film for decades and has an iconic shape; Simon Rodia's wonderful
Watts Towers; the
Griffith Observatory. The Griffith Observatory is gorgeous, doubly so because of its hilltop location.
My personal first choice for LA landmark would be that Googie masterpiece, the
LAX Theme Building. Instantly recognizable and it's seen by everyone who flies in or out of LAX. A companion landmark might be the
LAX sign and kinetic light pylons.
In summary, LA has tons of terrific landmarks but it's undeniable that the city has greatly benefited from the exposure afforded by Hollywood.
p.s. Please, everyone, Disneyland is not even located in Los Angeles County, much less the city. It's in the city of Anaheim, in Orange County. I'd love for LA to claim the Magic Kingdom but it rightly belongs to Anaheim. Same with the Angels baseball team. Give Anaheim its due.