Is there any manga that's taking place in a hospital/mental hospital? I'd prefer a mental hospital but an ordinary hospital is fine, too.

Maybe with some romance between two patients, a patient and a doctor/nurse? Anyways, romance in it would be fun... The important thing is that it takes place in a hospital/mental hospital, though.

Please let me know if you know anything that you think I'd like.

All of them take place in normal hospitals. I like the one-shot but the others are just so-so for me. However, they might fit your taste!

Romance is the main-plot:
The Skies of the Rising Half-Moon <-- There is an anime, too.

Romance is only a subplot:
The Best Skilled Surgeon
Iryuu - Team Medical Dragon

One-shot:
Present (Boichi)

First I have to think of is Diamond Dust (KANG Hyung-Gyu). It's a webtoon and it's not directly set up in the hospital, but because of the characters condition there is no way for them to stay away from it. It's a well developed storyline with likeable characters, even though it might be hard to face by times, but that's only because of the emotions being put into.

It's similar with Heaven's Door (HONGOU Ranko), which starts off in a hospital and then leads the two patients - being the main characters couple - out of it together.

Haikyo Shoujo - Chapter 3: Tansu Shoujo ("Chest of Drawers Girl") can also be of interest, although it's not revolving around a hospital and deals with the mental issues of the female main character during home visits by the doctor. HOwever, you might like the twists as the story unfolds and the drawings are pure eye-candy.

Nanairo Sekai - Chapter 4: Refrigerator Chocolate is again similar to the one above and brings you a bittersweet story. ^^

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"It's like love is a bonus in your life. Even without it, I'm just fine. I don't feel like pointlessly searching for it. You don't have to make yourself unhappy." (Ookami Shoujo to Kuro Ouji)

"Why does it rain?" - "To create drama." (Drops (Andou Yuki))

Wow, I read Nanairo Sekai just now because of your recommendation to the OP, Yankee-chan. Chapter 4 is really, really good (and sad)! I had to read the story twice in order to understand everything since there is a lot of ambiguity in there, but that is precisely what I like about it.

OT @_xyz_: Yes, the works of SAHARA Mizu (aka YUMEKA Sumomo) are pretty interesting, because what I remember most strongly from them is the bittersweet aftertaste of the emotions expressed in them. Often it's the style of art, but only seldomly the means being shown. So, I'm glad, that again someone else came to like that story~

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"It's like love is a bonus in your life. Even without it, I'm just fine. I don't feel like pointlessly searching for it. You don't have to make yourself unhappy." (Ookami Shoujo to Kuro Ouji)

"Why does it rain?" - "To create drama." (Drops (Andou Yuki))

I think Help!!, Limited Lovers, and Dr. wa Ijiwaru na Kiss de might fit.

Third story from Taiyou no Ijiwaru, A Strange Gene. Can't really say anything since it will spoil the story.

Birthday: set in normal hospital. It says shounen-ai, but I think it's more in subtle way.
Real

Hanbun no Tsuki ga Noboru Sora also has an anime which was pretty good

Try Kawamaru Shin's works. She did a lot manga with hospital theme. Though I don't really like her works since most of them kinda typical shoujo manga plot.