It doesn't HAVE to be a shoujo, but I prefer it to be realistic and have romance.
I want it to be school life as well.
I want the characters to be relatable and each character have their share of flaws and positive qualities, and I want the way they act to be understandable.

What I loved:
Koi Dano (and its prequel). It was so refreshing! The girl is dense when it comes to love not because she's dumb, but because she simply can't imagine somebody loving her.
I really was able to relate strongly to her: I am strong and perspective, and I don't take shit from people (she doesn't take shit from the main guy or any other person), but because I have many insecurities, I can think negatively of myself. I was also able to see myself in her best friend. She's not good at school, and she can be dumb, but she's not useless, she can be firm and she can catch on the feelings of Haru, and she was very firm with him and gave him a good scolding that he needed.
I was able to see myself in Haru too...I guess you get he point.

TL;DR something refreshing with realistic characters that explains the way they act and you can relate to, and that has very different characters; smart, shy, popular, strong, ambitious etc, but each character has flaws and positive points.
NO MANHWA PLEASE. I really can't like manhwa.

I HAVE READ HORIMIYA (Following it every month)
Please refer to my MAL so that you won't suggest something I've already read http://myanimelist.net/mangalist/Reee_no

Oh, darling, I don't think there's anything quite like Koi Dano Ai Dano out there.

But try,
Principal
Nekota no Koto ga Ki ni Natte Shikatanai.


And basically other works by TSUJITA Ririko

Beauty Pop

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I am not looking for the same story line, I am looking for realistic characters with a female lead like her.
For example, I think something like Six Half would work; the female lead is really strong, and the characters have their share of positive and negative sides (though since the story focuses on her, we see things in her own vision, so we can't really focus on the other characters that much).

There is also Tonari No Kaibutsu Kun: All characters have their shares of pros and cons as well! They are all teenagers who are learning to grow up. This is exactly what happened in Koi Dano.

Horimiya: I liked this manga because of the wide range of different characters! The female lead was smart and strong but she can be mean sometimes, as for the guy he was sweet and good hearted but he can be a pushover, and it is shown that it is not really healthy for them to act this way. They all have their own pros and cons, and the side characters are all with different personalities.

Do you have another one? I have tried this one but it bored me

I second Nekota no Koto ga Ki ni Natte Shikatanai. (it's hilarious but the male lead especially feels like he's much more mature than just a middle-schooler) and maybe Akagami no Shirayukihime (this one is more "shoujo" but very nice and realistic characters)

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Nulla in mundo pax sincera
"Always go too far, because that's where you'll find the truth." - Albert Camus

Only one volume long but I loved the realistic agony in Kiss, Zekkou, Kiss!!!

I read 3 Years by Rin Saito a few years back. I don't remember the personalities of the MCs so not sure if they are all realistic. However, I thought the ending was realistic and that's what stuck with me. Only one volume long as well.

Thanks! I will add it to my list.

Not sure if this is what you really want, but I suggest you to read Ame Nochi Hare (Bikke). It has a huge cast of characters, each with different share of flaws.

Ongoing:
Omoi, Omoware, Furi, Furare
Hatsu Haru
Yuugure Light

the scanlations is dropped, but it was really good and still my favourite until now, I had bought the tankoubon anyway. and I think fit what you looking for:
Platinum Garden (for me, it is on same level with Fruit Basket, but with wild female lead)
Gaccha Gacha

For some reason, Seigi no Mikata reminds me a lot of Koi Dano Ai Dano.

I think it is because it is episodic and also because the main character (?)--I put a question mark because the lead is shared between two sisters--is in a sense oblivious to the guy who likes her because she is so preoccupied with doing damage control on the havoc that her despicable older sister wreaks. Just like in Koi Dano Ai Dano, the guy becomes interested in her (the younger sister who suffers because of her older sister) because she is so preoccupied with managing her own life (mainly dealing with her sister) and as a result acts different than other girls (i.e. isn't chasing after him).

Another work that is by the same mangaka that has a refreshing lead is Kechonpa. She is in love with a guy that does not like her (she has a false demure, lady-like identity around him so he doesn't know who she really has become: brazen, confident, charismatic, stylish, street-smart), and rejects a guy (for now at least) who does like her (and knows her true personality).