If our place is in the Heavens, will we ever see or visit the new earth?

I like your question. It shows that you have put a lot of important facts together correctly about the Kingdom of God leaving you with a reasonable question. While the Bible may not give a direct answer, I do believe it does give enough information to answer that question. Consider these facts:

From Ephesians 1:9, 10 we know that God’s Eternal Kingdom will continue to have two locations – Heaven and Earth. But those two places are one Kingdom under the reign of our Lord Jesus Christ.

According to Revelation 21:1-16, the Lord Jesus will reign over this Kingdom from the city of New Jerusalem which comes down out of heaven and (I believe) rests on the earth. Interestingly, the dimensions of this city, includes its height. It is 1500 miles high. Outer space is less than 400 miles high. So this city reaches into the heavens.

Then from John 1:49-51, after Nathanael acknowledged Jesus Christ as the King of Israel the Lord said: “ … Because I said unto thee, I saw thee under the fig tree, believest thou? thou shalt see greater things than these. And he saith unto him, Verily, verily, I say unto you, Hereafter ye shall see heaven open, and the angels of God ascending and descending upon the Son of man.”

This means when the Lord Jesus sits on His throne in the New Jerusalem on planet Earth that the angels will be sent out (commissioned) from the earth, “ascending” into their abode (heaven) and then “descending” back to earth, perhaps reporting to the Lord and waiting for their next assignment. The Heavenly and Earthly portions of the Kingdom will be headquartered in the New Jerusalem here on Earth.

Therefore I believe that we too, will be required from time to time, to report to the Lord who will be here on earth and then leave to carry out our assignments in the heavens. If we get any vacation time, I will ask permission to visit places in the new earth. At least I think that will be possible.