So, how did they get together?
Does it address the tutor/student issue?
To borrow what someone else said:
Spock and Uhura definitely make for a good couple - similar enough in terms of implied intellectual ability and shared interests not to be baseless, but dissimilar enough to be complementary (the emotional/stoic thing).
There is chemistry as they like to work together and spend time together, you get to see them becoming friends so when they get together it feels organic and it makes sense.
Keep note that he was her teacher since her first year at the academy so in the movie they knew each other since four years. The tutor/student issue (if any) hadn't been addressed yet as they get together only in the last published novel that is the third year at the academy for Uhura and I don't know if by the time he still was her teacher or she was just his TA. I remember though at least one instance where it's implied that they hold back a bit because of that. Only when they're not wearing their uniforms she will call him Spock and he will call her Nyota.
If it's written for a young market I'm guessing there is no going where no Spock has gone before in it
it's subtle and in character....
true enough, the comics were more explicit with that shot of them talking in his quarters....