It occurred to me that in the whole anime, there is never any reason mentioned for why she falls in love with Yuki. I mean, the first Yuno from the first dimension loved him as much as the Yuno from the second dimension and so on the third (probably). But there was never any explanation for why that made her like him so much. Is there anything that explain that in the manga? or somewhere else?
Darjeeling's answer is right about the things that made Yuno falls for Yuki, but as far as I remember, there's deeper truth behind that:
Yuki wanted to go stargazing with his family, but his parent got divorced. So Yuno answered that she will be his bride, his family, so that Yuki's wish might come true. And to Yuno's answer, Yuki replied that they had to become adult first. The important thing was, later it was told that, at that time, Yuno's parents HAD already dies. She might seem OK, but she had actually fallen deep into despair, thinking that there's no future for her. And that was where the stargazing conversation happened, in which Yuki (kinda) promised to take her as his bride. Thus, that event gave her a new hope, a future as Yuki's wife.
So, without Yuki himself realizing, at that time, he saved Yuno with his words, and that event became a life support for Yuno.
I forgot the chapter of manga where that complete reason is revealed, but for sure it's not an early chapters, since a big, big secret
The story about how Yuno's parents death
has to be revealed first. Though I remember that when it was revealed, Yuki himself realized that
"So I've became her only moral support..." or something along that line
The reason is simple and a little bit ridiculous. It explain on chapter 5:
Because Yuki said he want to stargaze with his family, but his parent broke that promise to buy him a telescope because they got divorce. And then Yuno said that she will become his bride (so she can become his family) to watch a star with him. And Yuki (jokingly) answer that she have to wait until they're grown up, and Yuno accept that statement seriously.
these are pages on chapter 5, click to enlarge picture, page order: left to right
It's Yuno, she's yandere and crazy stalker. So I think it's reasonable for her to fall in love with Yuki because of such a reason like that
There's also the fact that we're dealing with 1st world Yuno here. That is, the untold story of the 1st World Survival Game. The 1st world Yuki might have been "cooler" than the 2nd world as he might have not relied on Yuno that much. Her feelings from that stargazing even might me reinforced more by the events of the 1st world Survival Game. And when she came to the Second World resulted to a "crazed Yandere Queen" Yuno for killing her beloved 1st world Yuki and not being able to resurrect him with the godly powers she acquired. (The key is to know that we're dealing with a mentally unstable girl who killed her adoptive parents and her lover.)