Based on the information you've provided, I can offer this: The word "acquaintance" is meaning a of "slight-knowing;" not necessarily a close friend, or somebody you know very well, but you're somewhat familiar or recognize the person in mention. So when it's used in the way you're inquiring "of their surrounding acquaintance," the impression is that it means that "somewhat familiar environment;" as if you're visiting somewhere you slightly recognize, but not absolutely in a common area. Hope that helps. :)

Can you provide the full sentence/paragraph that it's in, pls? There *can* be contextual differences in what it means, but just to be sure...