After some reflection: Bonus points for lesser orders of magnitude.
Or piggy-back on some similar endeavour and inject your haiku.
That's about the only thing that we know for a fact that can last for time spans in that range.
2) Convince a major manufacturer of stainless steel pans to stamp your haiku onto every pan they make.
Those should be findable in landfills for that long, and the advantage over the rock carving is redundancy.
3) If you don't care about ethics, create a highly-infectious retrovirus that encodes it in the DNA of every human it infects.
Humans might be extinct by then, but in that case there wouldn't be anyone to read it anyway, right?
Your best bet may be to come up with some mathematical representation of the haiku, like the arecibo message, and send thousands of copies of it into the solar system, and hope that 10k years from now we will have the technology to find and decipher them.
The 10,000 year clock project might have some useful ideas for you. Though buying a mountain in the desert, then drilling a hole in it is only possible with privilege and obscurity.
https://longnow.org/ideas/02017/06/07/how-can-we-create-a-ma... Scroll to the section "Projects that inspired the Manual For Civilization:"
https://longnow.org/store/proto-1-drawings-pbk/
"Long Now has compiled a record of all of the drawings made to create Prototype 1 of the 10,000 Year Clock into a new self published book.
Geared towards the mechanically inclined, this book is a highly technical document of manufacturing specifications. It also includes several math notebooks and spreadsheets that Danny Hillis used to make the underlying calculations for parts of the Clock.
Long Now hopes that the widespread distribution of these plans will ensure that the knowledge and work that went into building our first Clock prototype is not lost and that this will help the survival of the Clock itself and the long-term thinking it represents."
Any bites?
So much construction and development has engulfed the world. So you probably couldn't guarantee that anything even remotely close to a city now, will be the same that far into the future.
This means if you want to etch it into a rock it needs to be in a remote and dead part of the world which will likely never be developed, probably a desert. Or at the bottom of an ocean somewhere... But then no one will ever read it.
The best way to ensure it's still known that far in the future, is to make it popular somehow, copies will exist in history, the internet and throughout culture.
Think rock symbols of chilean dessert
Collections of its predecessor's web sites, geocities?
Where better to leave letters?
OP could have been haiku.
Please share your haiku!