Generally speaking, it is the man who goes to the woman's home first, but if both parties have no opinion, it is also appropriate for the woman to go to the man's home first. The specific decision depends on the distance between the two families and the time of the parents.
1. Distance
Since the two people have decided to see their parents, then we must ask their parents when they are free, if it happens that the woman's parents are not available at this time, the man's parents are free, then the woman first to the man's home is also a good way, and then wait for the woman's parents to go again.