So, the phrase intends to convey a sense of irony. "Of all places, it happened there." It's quite an interesting sentiment. Many times it is thrown in as part of a story, often a joke, that indicates a rather interesting twist and/or detail to the narrative.
"So there was a moment of healing at the bar, of all places." "They demonstrated such responsibility in, of all places, Washington D. C." "They played some good baseball, in the American League, of all places."
I wonder if the average churchgoer has this same sense of the world around them. We are often surprised when we see things happen, as though we are shocked that God has done something here, of all places. Or did we forget that the whole earth is filled with God's glory?
The context of the Great Commission, as well as the opening chapters of Acts, is that the whole earth is now encompassed with the glory of God through the Lordship of Jesus. No longer bound to geographic or ethnic boundaries, the gospel message extends to the earth now waiting for the people of God to carry it forward.
Of all places, this hurting and dirtied earth now witnesses to the coming glory of God. Perhaps the amount of our surprise is directly related to our lack of believing what God has done to restore the earth. Amazement will always be present, but we should be expectant of what he is doing.