Uhura has no children.. until a writer wants her to have some. So as
@Locutus of Bored said, having children isn't a pre requizet to being a happy woman. I know many women who don't have kids, and are happy with there husband/other.
Like people who spend 30 years plus in the military, for some its a calling, something that completes them. Uhura may be one of those, that like being out there with her friends/crew, exploring. If she has time for a relationship and family, thats up to her. Many a captain, Picard, Janeway, has lamented that its a bit lonely at the top sometimes. but neither of them stepped down to have a family. and seeing that some people like McCoy lived into his Hundreds and was still in starfleet, Uhura could have taken time off and had a kid, raised a family. Hell could be no father, many women go and get artificially inseminated for a kid, or by that time, with the danger of space travel, Uhura could have had a number of eggs frozen, and after Kirk died decided to have a kid. I'm sure by that time they would have created an artificial womb, so she didn't even need to carry the child.
So, after 2293 its all a big question mark that except for some easter egg that wasn't meant to be seen.
EDIT:
@ZapBrannigan Its all okay, I'm not ticked, it was a good topic to broach, and have a discussion about. and as always things get heated.
