Hmmm. This is asking for a lot, considering that humanity was on its path to discovering nuclear energy ever since the 1800's. Think Marie Curie, and various other scientists who experimented with x-rays, etc. It took until the 1940's for the technology to develop enough and for governments to be motivated to fund the research in order for the bomb to come along, but it would have happened sooner or later, even if WW2 had not occurred.
Alternate Power Source
I think it MIGHT be possible to skip nuclear energy if you give people some other POWERFUL energy source to exploit. For example the discovery of an alien artifact, or some strange material that we first find in the remains of a meteor that crashes on Earth (we use that material to get into space and harvest more, but at great expense).
Nuclear Power Without The Bomb
WW2 was averted somehow, and the scientists that stumbled onto nuclear energy did so in the context of a civilian scientific research setting, not military. That way they may give world nuclear power (by far our most powerful energy generating method), but avoid weaponizing it for a few decades. In the mean time, mankind enthusiastically researches new power sources and finds something even more powerful than nuclear energy - at that point you make some new tech up.
The thing to note is that neither of these scenarios actually excludes the creation of nuclear technology, or the atom bomb. Quite simply, a lot of scientists were having similar ideas about radioactivity, and one of them would have figured it out sooner or later, no matter what. Which leads to what is probably your best bet:
Aversion To Nuclear Power
Marie Curie or another scientist who first meddled with radioactivity is more successful than they should have been. One of their experiments accidentally irradiates a major European city and kills hundreds of thousands of people. The governments of the world impose a ban on all things nuclear, and severely punish any who explore that line of research. As a result, alternate power sources are explored: electrical motors, solar power panels, etc.
Good luck, hope that helped a bit.