Acadia National Park
Nauset Light, Fenway’s Green Monster, July 4th fireworks over the Esplanade.
For Montana, Going-To-The-Sun Road is probably the best single answer, assuming the entirety of a national park isn’t a single answer, but the road itself isn’t the main attraction, the view from the road is the main attraction, particularly over Logan Pass. Glacier National Park as a whole is the best-known park which is in Montana, as opposed to Yellowstone, which barely toes over into Montana and is mostly in Wyoming.
For an attraction where the man-made component is the main appeal, I’ll be a bit clever and say Pompeys Pillar, which is famous for having William Clark’s inscription preserved on it. It’s also in eastern Montana, and as such not in the Rockies, so going there is an excuse to show off the portion of the Great Plains in this state, which can be quite beautiful at the right time of year. (June, mostly, when it’s green from the rains, unless they have a real love of brown and light yellow.)
Mars Cheese Castle
I was going to say exactly this. Redwood trees might be in third place, but a distant third.
New Hampshire’s most iconic sight **was **a rock formation known as “The Old Man of the Mountain”. But it collapsed in 2003 and I am hard pressed to think of second one. Maybe an aerial view of Lake Winnipesaukee or Mount Washington. Or the Mountain Washington Cog Railway.
Thankfully, it’s forever preserved on the quarter.
That reminds me - are the landmarks and monuments that are featured on the state quarters what residents of those states would agree are “most iconic?”
^ Isn’t there a “Grand Canyon of New Hampshire”? Or is that a slogan every state tries to cop?
Mall of America.
I live in Arizona, and the Grand Canyon has already been mentioned.
In Victoria? Not much, come to think of it, unless you extend the definition to include wildlife.* Just about every iconic geographical feature or landmark building in Australia is in another state. Uluru/Ayers Rock is in the Northern Territory, the Sydney Harbour Bridge and the Sydney Opera House are in New South Wales. Hanging Rock, maybe, to literature aficionados.
*Sure, there’s kangaroos of various sizes, brush-tailed possums, and similarly famous Australian beasties. And snakes.
New Jersey? Statue of Liberty of course.
Now before the New Yorkers have a fit…
The most iconic event that took place was probably Washington crossing the Delaware and the Battle of Trenton. But Washington Crossing State Park is really just a scenic park on the river.
The Edison Tower where the light bulb was invented isn’t really that well known outside of the area.
The duel site in Weehawken has renewed interest because of a certain musical. It has a spectacular view of NYC but the monument isn’t very iconic.
I would probably go with the boardwalk down the shore. I would probably have to name the Atlantic City boardwalk as not the best but the best known. Can’t argue with Monopoly.
Pennsylvania – either artistic or photo images of the “three rivers” of Pittsburgh or the statue of William Penn in Philly. You could make a case for anything Amish but I think Ohio actually has a higher Amish population than we do these days.
As a native Ohioan, the most strikingly iconic site I know of is the Perry’s Victory and International Peace Memorial at Put-In-Bay on South Bass Island. You can see Canada from up there.
Ohio used to have lots of Amish, but they’ve mostly moved to Indiana or points west, I think.
Virginia, where I live now? Totally obvious: Monticello.
No Liberty Bell? The statue of Rocky? 
As much as burpo and I hate to admit it, Florida’s probably is Disney related, though I was thinking of the geodesic sphere at EPCOT.
Piffle.
The iconic Ohio attraction* has to be the Allen County Museum in Lima, where you can see Dillinger’s jail cell and marvel at the “Things Swallowed” exhibit** (of dopey things people swallowed and had to be retrieved by Dr. Yingling).
After that you can get iconic eats at City Barbecue.
*Unless it’s Cornhenge.
**They also have a display of albino animals.
Yep, Spaceship Earth was my first thought.
I live in DC, so not a state, but for us I’d say the Washington Monument.
The Hatteras lighthouse is a good call. My first thought was the Wright Bros memorial, but we’re probably splitting hairs. I’m pretty sure you misspelled Duke Bluedevil, though 
ETA… Maybe the Biltmore house?