Where will atheists go if they do not go to heaven or hell?

Answer 1

It depends on how it is read:

What do Atheists believe will happen to them?
Most Atheists are monists, believing that a person is only their physical nature, whereas most Theists are dualists, believing that a person has both a physical nature and a spiritual component. Monists argue that the brain is the source of a person's personality and essence and, therefore, when a person dies, and the brain begins to shutdown and decompose, that is the end of that person. (This is much the same way that dualists would conceptualize the destruction of a robot.) Dualists argue that a person's personality comes from an ethereal soul which can leave the body and go to an afterlife. Atheists who are monists take the monist position, while Atheists who are dualists (most commonly Buddhist Athiests) believe in whatever afterlife their tradition teaches.

What do Theists believe will happen to Atheists?
This entirely depends on the religion and even on the Theist himself. Most religions argue that Atheists will go to Hell or some other place of torture, but other religions do not believe Atheism to be sinful or to warrant pain if the Atheist is a good person.

Answer 2

Like everyone else, the will go nowhere. The Universe was without "you" for 15 billion years since it began and will be without "you" for the next 15 billion years until it is gone. Your fate involves the recycling of your components back into the carbon, nitrogen ad water cycles. Your personality and such is only hear for 100 years or so then it vanishes.

Answer 3

If there is a heaven and/or hell, there is a wide range of beliefs about what qualifies someone to go there.