It is a very random couple and completely ILLOGICAL. If Spock is going to be with anyone, it should be Kirk. Watch the Original Series and you could very easily see that.

Absolutely! They're adorable and tender together. The turbolift scene is my favorite: the way he collapsed on her shoulder and inhaled deeply as to stop himself from crying in her arms gets me all the times she understands his needs and doesn't push him. The transport pad scene is cute too I love the way he touched her forehead with his and the way he called her "Nyota". And his last words when he believed that he was gonna die where for her! I felt so sorry for him and i'm glad that he could come back.
They make totally sense to me especially in this alternative universe where he probably met her way sooner and got the chance to explore a relationship with her that the other Spock could never get.
Even in the other reality there is some flirtation between the two of them. And I can't help but remember a scene from “Is There In Truth No Beauty” when Spock mind-melds with Ambassador Kollos and then he starts to address Kirk as “best friend for many years” McCoy as “another long acquaintance” and then when he looks at Uhura he starts reciting Byron's poetry “She walks in beauty, like the night”!He reads poetry regarding her and we're talking about Spock here! Kollos had no idea about humans and couldn't know Byron he was simply addressing them according to what they meant to Spock as he was reading those feelings in Spock himself.
I know that the original creators wanted to put them together in the series too but they could never do that because she was black and those were the 60s.
I always thought that she's was the only woman that he could fall in love with and who could accept him for who he is. Being this Uhura a xenolinguist too further creates a link between them because she understands his language and can understand his culture it's easy to imagine how they met each other, gradually became friends and then something more. They're a great pair.
It's perfectly logical to have a relationship with someone that you love. He knows her since years and obviously appreciates her, she's beautiful and she has a strong personality and she's not intimidated by him like other girls might feel. His 100% vulcan father loved and married a human woman himself. Spock is half human. It makes totally sense.

they're so cute it hurts