"I kinda want to know about Keiko's love life." "Love life?" "Like who she's close with, who she's dated."
Literal
Keiko [gen-の] man-relations [obj-を] want-to-know [maybe-かな]. / Man-relations? / Who [with-と] close-is [or-とか], who [with-と] dated [or-とか].
男関係 ('relationships with men') is a compound used to gossip about someone's romantic history. The speaker hedges with ~かな ('I wonder, I kinda want to'). The listener's echo question '男関係？' asks for clarification. The answerer then uses 誰と ~ [explanation] とか, 誰と ~ [explanation] とか, with とか listing examples: 'things like who she's close with, who she's dated.' 仲が良い ('to be on good terms, to be close') is a fixed phrase using 仲 ('relations') as the subject.