I can definitely recommend a couple of good Cleopatra biographies, but with the caveat that although there have been many biographical treatments of Cleopatra, there is not that much to say about her.

Unfortunately, we have a relative scarcity of evidence regarding Cleopatra, either as a person or as a ruler. Compared to figures like Julius Caesar, whose early years and personal habits are attested to by a number of sources, we know very little about who Cleopatra is as a person. Despite being one of the most famous queens, we have no idea what her mother's name was.

Her reign also occurred during a rather poorly documented period in Ptolemaic Egyptian history. There is less in the way of Egyptian archaeology to work with as compared to some of Cleopatra's predecessors.

Because of how little there is to work with, there are not many good biographies that feel intimate. Most of them devote a good deal of time to Ptolemaic Egypt as a whole to provide context (and probably to pad the length a bit, let's be honest). All of them will probably tread familiar territory if you have already read up on the period.

Joyce Tyldesley's Cleopatra: Last Queen of Egypt is probably one of the best fits for your purposes. It spends the first chapter setting the stage by briefly discussing her immediate family, before going into detail on her life. Other topics, like Alexandria, the city where she spent much of her life, and the men in her life are also discussed when they intersect with the narrative.

Duane Roller's Cleopatra: A life also gives a very complete picture of her life and context, and has very detailed endnotes if you're interested in knowing what sources are used. However, it focuses on Cleopatra as a ruler, so it's really as much about the politics of the time as it is about Cleopatra.