I don't know how much this means as it has never been stated in the show or the movies, but according to Nichelle Nichols, the backstory that she and Roddenberry had created for Uhura included Spock being her mentor.
"Gene and I agreed that she would be a citizen of the United States of Africa. And her name, Uhura
, is derived from Uhuru, which is Swahili for "freedom". According to the biography Gene and I developed for my character, Uhura was far more than an intergalactic phone operator. As head of Communications, she commanded the corps of largely unseen communications technicians, linguistis, and other specialists who worked in the bowels of Enterprise
, in the "comm-center". A linguistic scholar and a top graduate of Starfleet Academy, she was a protege of Mr. Spock, whom she admired for his daring, his intelligence, his stoicism, and especially his logic. We even had outlined exactly where Uhura had grown up, who her parents were, and why she had been chosen over other candidates for the Enterprise
's five-year mission."
- Nichelle Nichols, Beyond Uhura - Star Trek and Other Memories
, p. 144-145
"I created a relationship between Uhura and Spock as being her mentor and the person she looked up to. Uhura was the only one who could play the Vulcan lyre and the only one who had the audacity to sing a song teasing Spock."
- Nichols in a 2008 inteview http://trekmovie.com/2008/02/14/trek...trekkies-more/