Many places around the world have an iconic “must-see” sight that a trip to that place would not be complete without a visit to that sight. For example, a trip to Paris wouldn’t be complete without a visit to the Eiffel Tower. In the US a trip to Arizona wouldn’t be compete without seeing the Grand Canyon. or Yellowstone in Wyoming. I live in Missouri and would say the most iconic sight is St. Louis’ Gateway Arch.
What would you say for your state?
Illinois, the Sears Tower. None dare call it Willis. I work right next to it, so I’m biased, but I still love seeing it every day every day even with the construction.
The Alamo, I’d guess. It’s a big state though, and there are plenty of other things that could be considered iconic I suppose.
The tourism board would probably like me to say Biltmore, but I’m going with the Cape Hatteras lighthouse.
Washington State.
I’d say Mount Rainier or the Seattle Space Needle
Waikiki Beach, with Diamond Head in the background
Manmade? Probably the USS Arizona Memorial. The quarter featured the Kamehameha statue
Portland, Oregon. Probably Multnomah Falls and the Columbia Gorge, also Crater Lake. Plus the entire coast but that might not be completely fair. 
Macinac Bridge. Or maybe Lake Michigan. It’s one helluva lake.
Cape Hatteras Lighthouse is probably the most iconic site, but I’d also add to the NC list the color tarheel baby blue. Even though it’s not a physical “site”, tarheel blue is the first thing I think of whenever an outsider mentions NC, and I live here.
Rhode Island
The Big Blue Bug
Some people might say it’s The Breakers in Newport, but you have to go out of the way to see that. Everyone taking I95 through RI can catch sight of the Big Blue Bug.
Hell you say?? The weatherball in Flint! Fucking legendary man! Guess what color it is now? Red. Red is for sexxaay.
In California it would have to be the Hollywood sign (for SoCal) and the Golden Gate Bridge (for NorCal). We are sorta like two different states.
There’s this really plain field in Plainfield where soybeans are grown. Ha, ha! Just kidding- It’s the skyline of the city of Chicago.
Meh, it ain’t unique. Grand Rapids has one too.
No visit would be complete without spending a few days at South of the Border.
New York – there are many. Statue of Liberty, Empire State Building, the Brooklyn Bridge and Niagara Falls are probably the biggest.
Ahhhhh! They just took our idea! Pffft. Grand Rapids. Which way do their streets go anyway? North? East? West? Nobody knows. Confused-ass city, if you ask me.
My state has already been mentioned, and I can’t think of a better answer than dalej42’s (unless the visage of Abraham Lincoln counts as an “iconic sight,” which seems a bit of a stretch). But another state with an obvious “most iconic sight” would be South Dakota, with Mount Rushmore.
I was going to say the golden gate bridge or Yosemite
Wisconsin’s would have to be either Lambeau field or the Dells. The former would be the most widely recognized. IMHO