Voter ID laws or election law in general is a big thing. These laws are state laws and governors enforce (or veto) them.
They have a word to say when it comes to opening times of polling stations. I remember that Rick Scott (R-FL) was criticized in 2012 for wanting some stations close on time despite long waiting lines to suppress Obama voters. He ultimately backed off.
Governors are also required to sign certification of election results. That may be relevant if the election is close. But I don't know whether the governor can refuse to certify results without a valid reason. Most likely not, especially if this goes before court.
Thanks for the answer! I hadn't thought of how governors can affect voters suppression.