hmm. Seems more people dislike Navigator than Explorer. I don't understand.
Navigator is pretty weak, but I think it's choice-to-cycle ability is decent in quite some situations. It can certainly cost $3 but I don't feel there is a significant difference between $3 and $4 anyways. Maybe the worst aspect is that it is a terminal so one might want to think it does nothing when you choose not to discard, and it does not provide as much utility to other cards that care about the content of the deck. I feel that is actually not against the card though, because it makes the card more situational.
On the other hand I feel explorer is a card I care less of. It is almost a vanilla silver gainer. That itself is fine for its power level, just I feel it is a bit boring. The collide-with-Province ability I feel is very situational since except with TfB mostly when you want gold you cannot make them reliably collide. Then it almost make this card a vanilla silver gainer + 1 trick pony. In general I am just not a fan of a very special effect that only has one usage.
I voted for pearl diver, haven, and explorer.
Pretty funny, they all appeared in a puzzle I did a few years back, which I am still proud of the solution.