David Zindell's Neverness (and the ensuing Requiem for Homo Sapiens trilogy)?
It doesn't match all the points of your description exactly, but has the far-future city, the young space pilot finishing training (with the hyperjumping and expanded awareness), the famous father, body-sculpting to fit in with a tribe of Neanderthals, etc..
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It doesn't match all the points of your description exactly, but has the far-future city, the young space pilot finishing training (with the hyperjumping and expanded awareness), the famous father, body-sculpting to fit in with a tribe of Neanderthals, etc..