Once upon a small town
Racket boys
Top Star Yoo-Baek

These also have a variation of the same trope:
Crash Landing on You
Our Blues
When the Camelia Blooms
When the Weather is fine

Top Star Yoo-Baek It was fun!

When the Weather is Fine Park Min-Young goes back in the town she grew up.

Once Upon a Small Town It was a cute little drama.

Racket Boys But it's not a rom-com. It's a family with their 2 kids who moves in the countryside. The parents are badminton trainer and they live with their athletes. It was a great drama!

Summer Strike It's young woman who is tired by the city life and goes in the countryside. But it wasn't really a healing drama, they were too many mean people.

The Man of the Vineyard It's quite an old drama now, I don't know how it aged.

I only have one winner and recommendation
Mr. Gu : My Liberation Notes.

Once Upon A Small Town is the obvious choice here. It’s very cute and sweet - there are even puppies! It’s also a quick watch, and you can feel free to skip the annoying screechy ajummas with no loss of story if you like.

The sageuk version of this trope is probably 100 Days My Prince. The CP may not be a city-dweller in the traditional sense, but you get a lot of the same small town folk hijinks at his expense. I thought it was really fun!

If you're up for Cdramas, Meet Yourself fits the bill and is a wonderful drama.

Modern Farmer - members of a band move to the countryside to farm and earn money to fund a comeback

When The Weather is Fine - FL had an extended stay in her hometown after her career took a nosedive in Seoul. It wasn't so much adjusting to life in the country, but more about rediscovering herself and the people there.

Do Do Sol Sol La La Sol - rich FL lost everything she had and opened a small piano academy in the countryside. More than adjusting to the area, she had to get used to being poor.

Island - totally different genre, but chaebol FL got stuck in Jeju island

Once Upon a small town
Hometown Cha Cha Cha

I highly recommend c-drama Meet Yourself, already mentioned by @stacya .

And of course, Crash Landing on you.

Lee Min-Ki was hilariously fish out of water as a cop from Seoul sent to a small town as a disciplinary measure in Behind Your Touch.

Two more sageuk versions of the trope:

Poong the Joseon Psychiatrist (season 1)
Bossam

Fantasy Couple
My Husband Mr. Oh
Haeundae Lovers

What Star Did You Come From

I guess to some extent this also applies to the ROMANTIC DOCTOR TEACHER KIM series. At least, it’s always a big deal for the young doctors from Seoul to be assigned to the „small town hospital“. 🤔 However, I don’t remember any of the usual „village shenanigans“ 😂 - like (m)any external characters… The hospital crew is almost always among themselves, be it at work or at that very small bar run by the anesthesiologist (wasn’t it…?). But do we see „village life“? I don’t think so (or I simply don’t remember😅).
But the fish out of water premise is there!

The Good bad mother had two city gangsters who went under cover as farmers and were comedy gold but they were side characters in a quite dark drama.

Thank You (2007) - very poignant drama
Crash Landing On You - fun and romance
Top Star Yoo Baek - campy and fun
100 Days My Prince - rural area during Joseon period

Diary of a Prosecutor

“stuck living in a seaside village” is the key phase: SUMMER STRIKE (2022). My word, what a collection of horrible people.

100 days my price works for sure!!
I am really going to stretch it an say parts of Attorney Woo. They spent a lot of time gaining experience and love of the countryside. And relationships are stating. My found respect for the circumstances and they could help.

I will go to you when weather is nice and Meet Yourself are gems. In It's okay not to be okay they move to countryside /small town but country side living is not exactly its main feature.

Great choices, Beanies!

-When the Camellia Blooms, since the owner moved back to a small town to get away from her ex-husband, famous baseball player and fell for the local policeman.

-Pachinko had the country girl (actually Jeju) move to the big city in Japan.

Do Do Sol Sol La La Sol - Lee Jae-wook's first role as ML. Whatever you do, skip the last 15 minutes of episode 16. It is set in the beautiful fictional town of Eunpo which is the real-life Mokpo in Korea. 😊

Link: Eat, Love, Kill - no recommendation required other than Yeo Jin-goo ... as chef.

Warm and Cozy - no recommendation required other than Yoo Yeon-seok ... as chef.

Once Upon A Small Town - short, sweet, cute, bicycle riding cop FL, vet ML, animals and a peach farmer with a coffee machine!! What's not to love.

My Perfect Stranger - countryside in 1987 with a side of murder.

Island - well it is Jeju (as never seen before) and FL is stuck there so ... 🤷‍♀️ ... viewer discretion advised. 😉

Our Blues - also set in Jeju. Again proceed at your own risk.

The Good Bad Mother 🤐

Heirs - second lead Young-Do looked and found his mom.
When a Man Loves (2013) - Main hero meets his mother (and eventually his father) is second part of story.
Both doramas were rather famous, I generally liked them.

A subsection of this trope is the visit to the outhouse—with the city slicker disgusted and/or terrified to use it. I remember this kind of scene with Jung Il-Woo in High-End Crush. I can picture several other instances, but don’t recall which dramas they’re from. In one of them, the scaredy-cat insists that the host stand guard outside the outhouse and whistle or sing while he’s doing his business.

Just wish to add an ‘oldy’ from 2006 - Which Stars Are You From starring Jung Ryeo-won and Kim Rae-won. Lovely chemistry of the two leads and JRW’s country pumpkin is winning. I remember pulling an all-nighter to finish it in one go.