We come full circle. In our sketch of the NT evidence, there is enough evidence to conclude that heaven — at least for Peter and for John — is not the final place. The final place is the new heavens and the new earth with a new Jerusalem.
Rev. 21:1 Then I saw a new heaven and a new earth; for the first heaven and the first earth had passed away, and the sea was no more. 2 And I saw the holy city, the new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband.

Rev. 21:10 And in the spirit he carried me away to a great, high mountain and showed me the holy city Jerusalem coming down out of heaven from God.
This leaves this question: Does Jesus teach a new heavens and a new earth? Not in so many terms, but this leaves then the probable reality that for Jesus the word “kingdom” refers both to the reality of God’s presence now and it also refers to the manifestation of God’s final kingdom as well. Hence, in the word “kingdom” we have both now and the new heavens and the new earth.
One point I would suggest is that not everyone used words with the same meaning. It is not like the earliest Christians had a pocket lexicon with words defined by Jesus and they pulled it out at just the right time to get their terms just right. Instead, we have a variety of authors/speakers using terms that overlap and terms that are defined differently. Which also means the NT writers didn’t have one set of ideas for the future that were tied down tightly with specific words. They had an inspired vision of what God would do and each expressed the vision in ways that resonated with that culture at that specific time.