As humans, we are predominantly right handed. In North America we drive on the right side, tend to walk on the right side and I suspect that this right side bias carries over into many other areas that we are not even aware of. I learned as a young police officer that if I was attempting to catch a driver that I had lost sight of I would be more successful if I turned right instead of left at the next intersection. A smart cyclist will take advantage of this situation by always riding on the right-hand side.
A very high percentage of cycle crashes involve turning and crossing in traffic at intersections. These are often busy places where drivers are trying to track many moving objects at once and determine a safe path for their intended direction of travel. Cyclists tend to be a smaller target that other vehicles in traffic and tend to be ignored. If you are riding on the wrong side drivers are not looking for you there and this compounds the risk further. Wrong way riders can have up to four times the collision risk than those who ride properly on the right.
Riding on the sidewalk is also not safer than riding on the roadway. Drivers are watching for pedestrians on sidewalks, not fast moving bicycles. You can increase your risk by two to nine times if you ride on the sidewalk. There is also a significant risk of colliding with pedestrians.
Ride in a straight line and choose your lane position wisely. If you are travelling at the speed of surrounding traffic ride in the lane itself. If you are slower, ride on the right side but do not hug the curb. Drivers will try to take advantage of the room to squeeze by if you don't take control of the situation by riding in the lane where there is no paved shoulder.
Finally, be courteous. Like slow drivers, give others the chance to pass.