voltages in transmission lines
Where exactly does this wave travel? Is it along the top or the bottom conductor?


Both. The potential difference or voltage that evolves according to the wave equation is a potential difference between the two conductors. It doesn't exist on one conductor without reference to the other one.


  On the other hand, if both waves travel on the top conductor, how isn't there interference? Or is that what causes there to be a standing wave?


You are correct, the standing wave is the result of interference between the forward and reverse travelling waves.