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.

Officially https://en.wikipedia.org/wiki/Santa_Claus_(sculpture)

Locally: butt plug gnome

Titty Sphinx

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

My friends and I always referred to the Salesforce Tower as the "Sales Dong"

It’s not a monument, but I drive by California’s boobs pretty often

San Onofre’s nuclear power facility

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.

Posankka. Pig duck.

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

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!

Sterling Heights, Michigan has the golden butthole

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.

Bierbrunnen aka The penis or cock They even put giant condom on it for world HIV day once.

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

Reality Checkpoint

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)

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.

Oh so THAT'S where my sleep paralysis demon lives.

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:

In Perth, WA we have the Cactus, the official name is "Grow Your Own", but it's definitely The Cactus.

Monumento a Luis Battle Berres
We all call it.so much "Los cuernos de Battle" (Battles's Horns) most don't even know it's real name.