It's not exactly a landmark or monument, but National Defense Head Quarters in Ottawa has a few:
The Cowering Inferno
The Shit show on the Rideau
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It's not exactly a landmark or monument, but National Defense Head Quarters in Ottawa has a few:
The Cowering Inferno
The Shit show on the Rideau
In my state, Colorado in the western US, we have this statue.

Official name: Blue Mustang
Our name: Blucifer
The German city I used to live in has an oversized pedestrian overpass with three large openings or holes. It never had an official name (as it was never intended as a monument or sight), but right from the start it was locally known as the Elefantenklo ("elephant loo"), or E-Klo.
These days it's often considered Gießen's most well-known landmark, which... tells you something about the place.
German wiki with photoa: https://de.wikipedia.org/wiki/Elefantenklo_(Gie%C3%9Fen)
Sterling Heights, Michigan has the golden butthole

Bierbrunnen aka The penis or cock
They even put giant condom on it for world HIV day once.
In Perth, WA we have the Cactus, the official name is "Grow Your Own", but it's definitely The Cactus.

We also had The Kebab (officially the Ore Obelisk), but it was removed for maintenance years ago, and recently forever replaced with an astronaut, unfortunately.

I used to go to uni in this city which had the "horse's butt" / "horse butt". It's just a regular horse soldier kind of statue, nothing special about it; however, due to it being right in front of one of the university buildings, among students it (or the surrounding area) was called like that. I doubt the creator had the title "horse's rear" in mind.

Idk if it classifies as a monument, but I present touchdown Jesus from southern Ohio.

Isn't it gone now? I recall that God was not amused, and it burned down after a lightning bolt hit it.
Yeah It was struck by lightning and burned down. They rebuilt it a few years later with a doofier Jesus.
There was a whole debate amongst the locals ala “is it right to rebuild it?” “Was this a message from god?”, some people were mad they rebuilt it, everyone hated the new design, then everyone moved on.
People over the age of like 30 still call him touchdown Jesus. It’s not the same anymore but it’s what immediately came to mind when I read the prompt.

100% what I was after when posting. That's a great name haha.

Titty Sphinx
Yes, I can see that. What's the unofficial name though?
We have The Bean here in Chicago, and the artist hates that we don’t call it “Cloud Gate.”
But, like, look at this thing. It’s a bean.

Also important to note that the artist fucking sucks, so we live calling it the bean to piss him off.
If there’s one thing the people of Chicago hate, it’s the Packers.
If there are two things all the people of Chicago hate, it’s pretense.
If there are three things all the people of Chicago hate, it’s ketchup on hotdogs.
Officially https://en.wikipedia.org/wiki/Santa_Claus_(sculpture)
Locally: butt plug gnome
A red version was unveiled in May 2018 in Oslo, Norway. The unveiling was done by a man pulling off the cover, suspended by an overhead crane with hooks through his skin.
Hey uuh what the fuck
Welcome to Norway, home of the stave church, cheese slicer and death metal!
Oh, and this is in my home town:

Norway can be extreme sometimes (maybe that's why there's an Extreme Sport Festival).
Just last night I learned what a stave church was, and that many of them were burned down in arson attacks by people in the black metal scene in the '90s. Now I learn that what I've always known as a cheese slicer is from Norway. (Funny coincidence about who settled here...)
It's not the cheese slicer I fear. It's the cheese. Brunost is... different.
It's different, but also really good! If you had it by itself, it's not a good experience. From what I've heard, the best way for foreigners to try brunost is on a waffle. You should try it!
I was in Norway some years ago, visiting a friend in her summer... hut? Everything about it was great, but that cheese was not mine 😅
If someone calls it their summerhut (hytte), they have at least one more, used for the winter. So your friend is rich. Many people only have one, and those who don't (like me, grew up very poor) are usually considered "lowered"-class.
Norway is, unfortunately, mostly about status and class, which is fucking horrible... First thing people ask is "what do you for a living" to figure out how much respect to give you. I hate it! I remember at a party with rich people; when asked what I did, I told then I was retired. They then asked if it was "early retirement because you cannot work?" I smiled and said no, I just don't need to work. They would then talk to me about investments etc instead of not talking to me at all... Fuck these people!!
Na, it was just my lack of English (or Norse). It was more like a cosy shack with an outdoor toilet on a cliff by the ocean. And she has inherited it and is using it with the whole family. She's just a broke German/Norwegian gal 😅
OMG! That sounds exactly what a hytte should be! Small shack with amenities - not two tv rooms, sauna, jacuzzi etc. Sounds like she has my dream hytte 😎
It was great, yes. Sadly she was the friend of my now ex wife, so I'm probably not going there again.
That's supposed to be a CHRISTMAS TREE? hahahaha
Rotterdam represent!
Talus Balls / Big Balls / Shiny Balls
It's the Talus Dome, which was dumped cynically by a loud highway bridge on a steep hill because there was a mandatory art % budget that had to go into some public projects at the time IIRC.
Most everyone makes fun of them, although the look kinda cool up close. Also a guy got trapped inside semi recently lmao: https://globalnews.ca/news/9773983/talus-balls-dome-art-west-edmonton-repairs-delay/
Oh balls!

It’s not a monument, but I drive by California’s boobs pretty often
San Onofre’s nuclear power facility
We always called em the nuclear tities
Our university mascot is Bucky Badger, sometimes expanded to Buckingham U. Badger. It's gone now, but that explains why we called this sculpture Buckingham Phallus:

It's like something from the bone temple.
Atlanta has the BAY Bridge. Atlanta is nowhere near any bay of any kind and it's just a bridge over the interstate. BAY is actually an acronym so the real meaning is the Big Ass Yellow bridge, although the news and other "clean" sources will use the term but say it's the "big and yellow" bridge.

Oh so THAT'S where my sleep paralysis demon lives.
Oh, don't worry, in real life it was just a crime ridden street hole with lots of heroin addicts and drunk people.vomiting.
My friends and I always referred to the Salesforce Tower as the "Sales Dong"
We are more basic and stick to "penis tower". A true to life embodiment of capitalism.
Ha! We call it the Battlestar.
Always thought it looked like the Battlestar Galactica standing straight up.
The big phallus in San Francisco? Sales Dong is a great name.
Actually the official name with a fun pronunciation:
Champoeg State Park.
Champoeg - Sham-pooie.
https://stateparks.oregon.gov/index.cfm?do=park.profile&parkId=79
I had my high school reunion there. Lovely in the summer, dreary in the winter.
Posankka. Pig duck.

Pig Hill. Legend has it that a family with major facial deformation (pig faces) due to inbreeding lived up there in the woods and killed hikers who got too close to their homestead.
A local filmmaker made a horror movie about it in the past few years. I haven't seen it, and I don't know if it's available online.