Earth's surface is finite. Yet, it has no end. If you start off in one direction and you keep going, you would never reach an edge. You would, however, pass over the same spot every 40,000 km.
Earth's surface is a 2-D example of a surface that is finite, yet has no edge.
The same concept does exist in 3-D. There are 3-D geometries that are finite, yet have no edge. And yes, if you were to start off in one direction and try to go forever, you would, in such a geometry, pass through the same spot after a while.
In the real universe, you would have at least two problems:
1) by the time you come back to the same spot, things would have moved around so much that you would not recognize anything.
2) Because space itself is expanding, the distance left to cover, before returning to the start would keep increasing instead of decreasing. We know that the universe is at least 3 times bigger than the portion we can see. If that is all there is to it, then the circumference of the universe would be (let us say) around 120 billion light years (in comoving coordinates).
By the time you travel 10 billion light-years, the remaining distance would NOT be 120 - 10; it would be somewhere around 140 or 150, because space would continue to expand everywhere during your travel time.