Well, first, I'd point out that Heaven is not the kingdom of God. When Jesus says the kingdom of God/Heaven He is not talking about "Heaven", but God's reign. That is, He is talking about what it means for God to be King.
Second, it depends on what we mean by "Heaven". In Hebrew the word is always plural "Heavens", and in Hebrew (and Near Eastern) thought there were seven heavens, likely due to the significance of the number seven in the ancient near east being associated with the sacred indicating completeness. We shouldn't take the idea of seven heavens too literally, as though we can map them out in some kind of celestial topography. Fundamentally the important thing is that ancient people often envisioned the gods dwelling up in the heavens, however the Israelites frequently spoke of their God dwelling higher than the heavens, or above the heavens: God transcends everything, so Solomon could say, "The heavens, not even the heavens of heavens can contain You, how much less this house which I have built." The phrase "heavens of heavens" is similar to similar expressions such as "Holy of Holies" and "King of Kings", the literal meaning is the highest, greatest, or most sublime of something. Thus the "heavens of heavens" is the highest or greatest heavens, of which there is nothing greater or higher--and here God is greater than even this.
So, in one sense "Heaven" or "the heavens" can simply mean "everything we see when we look up and that which is beyond even that", ancient people didn't have the same view of the earth and its relationship to the rest of the cosmos as we do today, so it would be anachronistic to try and force our modern cosmological model upon the ancients.
All of this should help us understand that that "Heaven" as a concept is an attempt to speak of divine sublimity--the utter transcendent greatness of God beyond and above all of creation. Thus, the idea of "Heaven" as being God's abode, as we speak of God's throne in Heaven, or Christ being seated at the right hand of the Father in heaven, or of the angels and saints in Heaven before God's throne all must be understood within the linguistic-cultural lens of the people and time. It would be wrong to try and insist that God literally sits on a chair somewhere in the universe, or that Jesus is literally seated on another chair right next to the Father, or any of these such things. The throne of God speaks of God's sovereign authority and Kingly rule over the whole universe as the Maker and Ruler of all things; Christ being seated at the right hand of the Father is to speak of Christ's power and authority as the Risen Lord and Messiah. When we speak of the angels and saints being with God in Heaven we mean they are indeed present with the Lord, but in what sense that can be comprehended by us is fundamentally beyond our ability--but we do have the hope and promise that those who are in Christ will be with Him between the death of the body and the resurrection of the body.
Heaven, ultimately, isn't about where, but Who. It is about God's presence, God's rule, God's power, and God Himself. And we can't point to some place "out there" and say "Hey, that's where God is" because, in reality, God is everywhere. There is no place God is not. He fills all things, and is beyond all things.
-CryptoLutheran