The first question: what would a world without nuclear weapons look like? I am not too sure about how it works, but I know nuclear weapons were a huge leap in understanding of physics, and I'd assume that there are many technologies today whose existence, in some way or another, require the same sorts of understanding that led to the nuclear bomb. Obviously, nuclear power would not be possible. On the other hand, what kind of technology could have been developed in a world without nuclear technology? This is especially important as regards the Internet, microprocessors, computer technology...
The second question: what kind of developments, beginning no earlier than 1920, could have led to a situation in which nuclear weapons were not invented - at the least, not as early as in OTL? Without completely destroying humanity (difficult, anyway, considering a lack of nuclear weapons!), how late could it take for nuclear weapons to be developed? The 1960s? The 1990s? Maybe physicists are persecuted widely as contrary to good Christian values? Maybe Albert Einstein never determines that it is necessary to give up his pacifism?
Thoughts!