The kingdom of God is within you
Neither shall they say, Lo here! or, lo there! for, behold, the kingdom of God is within you.
What is the “Kingdom of God”? Some newer translations put this as “God's imperial rule” – but I think this has no flow to it at all. Yes, “Kingdom” is a male-centered phrase, but ancient Judea was a male-centered society. Just as in English we have no good, gender neutral pronouns (“his/her”, “s/he” are just really awkward), one must make allowances for the limitations of language and current/local zeitgeist.
Initially, based on then-current Jewish beliefs, the Kingdom of God was when the Messiah would return to free his people from captivity. As Christianity developed, the Kingdom of God was to be when God would raise the dead (bodily) and there would be no more pain or sadness.
The first generation of Christians believed that the Kingdom of God would start within their lifetimes, and so everything was urgent and imminent. As the decades and centuries rolled on without this happening, this notion began to be adjusted to a more other-worldly view which has developed into the common idea of heaven.
If you ignore the centuries of apologetics, you can perhaps see that the Kingdom of God is the union of the human with the divine – and this is in you! I've always wondered: how much more explicit did Jesus need to be? It's all right there – straight from the source (or at least as close as we can get).