Something man-to-man is straightforward and personal. If your dad has something very important to tell you, he might sit you down for a man-to-man conversation.
You could also describe a man-to-man talk as being "one-on-one" or even "woman-to-woman," since man-to-man obviously excludes anyone who's not male. The term has an implication of extreme honesty: "It might hurt your feelings, but I think it's time for a man-to-man chat about your grades." You can also use man-to-man to mean "player to player," a common sports defense strategy in which every player guards one specific opponent.