I do believe your right to travel, inside the borders of the USA, is constitutionally protected under your fourth article. RealID and the requirement of a license could be argued that this is an unconstitutional tax. Wouldn't win or hold up, but that fight would be a fun one to watch. That same section two bit is used to argue for national concealed carry all the time.
I think your right to move around is protected, but the method by which you do it is not (strictly speaking) guaranteed. Again, states can make you pass a test to drive. States are generally not allowed to make you take a test to be allowed to vote.
I believe there are instances where voter ID has been struck down have (in part) dealt with issues around getting ID cards. Working from memory (which could easily be wrong), i think there was a case where having to purchase a state ID card meant that requiring the cards to vote was a burden. But if the state simply issues ID cards then it was not since there was no 'tax' before you were allowed to vote.