Then I give you the steps of the Mirabell Gardens in Saltzburg - I visited them precisely so I could sing Do-Re-Mi.
And the Cathedral steps in Girona, Spain, for the epic scenes from Game of Thrones:
My mistake.
The Hollywood High 16 stairs, with central rail, is famous for skateboarding and skate videos. I recognize it, even though I can’t recall any specific video or movie where I’ve seen it.
The stairs of the Bradbury Building in Los Angeles have been featured in innumerable films, most notably Bladerunner, DOA, and Double Indemnity.
The twisty, forked staircase inside the Livraria Lello bookstore in Porto, Portugal is said to have inspired J.K. Rowling’s descriptions of Hogwarts and the Flourish and Blotts bookstore in Harry Potter.
Of course, that’s not the only set of stairs made famous by Game of Thrones. There is also the Jesuit Stairs in Dubrovnik, Croatia featured in the walk of shame scene.
Does a fire escape count? If you’re a fan of Pretty Woman you can see where the ending was shot at the Las Palmas Hotel in Hollywood.
Don’t know how ‘famous’ they are, but there is an epic set of natural rock steps constructed on the grounds of the Presbyterian Conference Center in Zephyr Cove, Nevada. They go all the way from the top of the property down to the level of the lake and are quite spectacular. Unless you had to shovel them in the winter.
Can’t find a picture.
The Grand Staircase on board the Titanic, made famous in the movie Titanic (and others too, I believe).
No photo of it is known to exist, but this one was on the Olympic and is said to be identical.
The clock sculpture is titled “Honor and Glory Crowning Time.”
Since we’re looking for steps that were used as movie locations, I’ll point out that the Filbert Steps in San Francisco (which I mentioned earlier) were in Dark Passage (1947), The Killer Elite (1975), Petulia (1968), The Laughing Policeman (1973), and The Sniper (1952).
Another famous set of San Francisco steps are at Alta Plaza Park. Several cars were driven down them during a chase scene in the movie What’s Up, Doc? (1972). The scene was shot without a permit, and the damage that was done to the steps is still visible today.
The Dog Leap Stairs in Newcastle-upon-Tyne. Used in Get Carter and The Fugitive.
But to Dire Straits fans they will always be the place of Mark Knopfler’s early teenage romancing.
When EMI House at 20 Manchester Square was demolished in 1999, there were reports that the famous stairwell was disassembled and reassembled at the new EMI HQ in Hammersmith, but I can’t find any evidence of that.
Statue of Liberty stairs to the crown. Some photos here. I remember struggling up those steps as a little kid. One thing added in the 1980s renovation was an emergency elevator to the crown, to bring down people in stretchers. If I recall (from a book about the renovations), there was room for one standing up.
The Exorcist Stairs. An otherwise nondescript set of stairs in Georgetown made famous in The Exorcist. They’re made to get from street level down a cliffside to a small parking lot below. I was fascinated by this movie and in 1988 happened to be visiting DC for an Army 10 miler. This was before internet, GPS, and satellite photos so I had to study a street map and make a best guess as to where it was. I found the house! Nothing to mark it as the house the movie was shot in, nor the stairs (though now I read the stairs are a historical landmark.) The stairs ended at the back side of a gas station parking lot, nothing too exciting, but I was thrilled I got to walk up and down them.
As mentioned in the OP. Take a look at an early scene in the movie. The camera (apparently filming from a helicopter) closes in on the Francis Scott Key Memorial Bridge, which goes from Virginia, across the Potomac River, to the Whitehurst Freeway NW. This is about a half a mile from 3600 Prospect Street NW, which is the house pictured in the movie. (This is only for exterior shots, of course, since interior shots were done in a studio.) Here’s a map of this:
Incidentally, the first time I saw The Exorcist, long before I moved to the D.C. area, I didn’t get any idea where the stairs were, since I knew little about the geography of the area. The second time I saw it, after moving to the D.C. area, I watched that early scene and was able to immediately work out approximately where the stairs were supposed to be. I drove there a few days later and quickly found the stairs.
The steps of the New York State Supreme Court building in Lower Manhattan have been featured in countless legal dramas, Law & Order episodes, and so on. It’s enough of a cliche that The Onion lampooned it here:
MeTV this last week showed episode 4-13 of Monk with a chase scene on a steps on a steep San Francisco street. Monk pauses the chase as he counts the steps. From what I can tell it’s Fillmore and Broadway (but I may be wrong). They are highlighted on this Take the Stairs page of famous San Francisco steps. I’d be curious if that’s the right place.
Speaking of natural rock steps, we have those on the trail to Angel’s Landing in Zion:
Perhaps not that famous in their own right, but highly memorable to anyone that’s traversed them.
According to Bill Cosby, a portion of Santorini’s Karavolades stairs figures into the plot of an episode of “I Spy”. These are the stairs he’s referring to during his routine about shooting on location in Greece.
