RFK probably waits till either '72 or '76 to run for President, depending on if Nixon is seen as unbeatable in '72 in this timeline.
Bobby somehow getting to sit out 1972 and yet remain viable for 1976, that's a thing hereabouts, I think.
An ATL Watergate would probably have RFK as Nixon's Enemy #1, but IMO he'd be more cautious than gleeful. After all, Nixon's methods weren't terribly different from his own.
A living RFK is in a world of trouble if the revelations about the Diem coup, and the assassination attempts on Castro, all come out as per OTL. (And the Diem reveal isn't just the Pentagon Papers; it first started to come out in an overlooked memoir by one of the Camelot advisers published in 1965!)
If the coup is fully litigated in anti-Bobby Dem politics at some point, it'll put him on the spot, make him look no different than an LBJ or Nixon official defending their boss' actions in the war.
If Mongoose is fully litigated, the Democratic insurgents will eat him alive, even accounting for the fact that too much culpability for illegal actions against Cuba was attributed to RFK posthumously IOTL; of course, a living Kennedy won't do himself any favours by strongly disavowing knowledge of Mafia involvement in that illegal CIA war, a war which he must admit to having run...
This is before we get to his complicity in some of Hoover's shenanigans, not to mention impotence in the face of other FBI outrages.
Long story short, this stuff feeds into my belief that Moonbeam sucks a lot of the air out of RFK's presidential ambitions come 1976, if they still exist at that point.