The sentence: "Wait, so you just walked to the hair salon?" gives a similar meaning to "Wait, so you just walked on over to the hair salon?" but the second is used more for a situation where it would be unexpected for this person to go to the salon. "on over" makes it seem like the person saying the sentence is surprised that this person will go the the hair salon.
Person A: "What did you do when you saw the Hollywood movie star in the shop?"
Person B: "Well, I just walked on over and asked for their autograph!"
Person A wasn't expecting Person B to ask the Hollywood movie star for an autograph but Person B was brave and "walked on over".