I made up the sentence, but I can't be sure how we actually moved:
We traveled around the edge of the city in a circle? Or we traveled in a circle within the city? Or we traveled about/around within the ciry?
In the sentence as it stands I think the logical interpretation is the first one. To convey the sense of either of the other two you'd have to say something like: "We circled/rode around in the city on our bikes"