First of all the jury is still out on whether even Christians go to Heaven. The Bible is rather ambiguous on the subject. The same goes for Hell. Most of the imagery we have for these places has developed over the years since the Bible was written. Christianity offers salvation it is true, but speculation on the exact nature of that salvation is just that – speculation.
I think the reason we sometimes have the false sense that God is so far away is because that is where we have put him. We have kept him at a distance, and then when we are in need and call on him in prayer, we wonder where he is. He is exactly where we left him.