If you jack up the front, grab the wheel at the 3 and 9 o'clock positions and shake back and forth. If there is play, it is most likely the tie rods. If you grab it at 6 and 12, and it rocks, most likely ball joints. My car does the same thing on wet parking structure surfaces...I think its because our cars are rear wheel drive, and on the wet ground, it is easier for the tires to slide over the surface at full lock rather than turn over it. I bet it will do the same thing on the left tire, but you only go take right turns (or left) in your parking lot, which is why it seems to only be one side.