Agreed! I don't have too much to add to the comments/answers already here. In your examples, "around" is used to mean going to and fro without specifying a particular location.
A similar example might be something like:
"I'm tired of being cooped up inside! I just want to walk around for a bit." It would be similar to "dar una vuelta"; or to go for a walk. I agree with Jose's explanation using "recorrer" or "merodear."
Another common example is "to run around," often used to refer to children or pets: "The dog needs to unleash some of this pent-up energy or we'll all go crazy! Let's go to the park and let him run around for a bit."
However, as David said, if you add the location afterwards, "around" will refer to that object or place. I would add here that "around" in this case could mean a couple different things:
1 - to go about here and there in/near the location of the object, similar to the above examples but just more specific about where the action is happening. For example: "take a walk around the neighborhood" - "dar una vuelta / un paseo por el barrio"
2 - to go in a path along the perimetry of an object or place, encircling the object or place. For example: "the cat has a ritual of walking around its bowl of food three times before it eats."
Hope this helps!