Thanks for the feedback guys. I reworked the Lost City Explorer into Hidden City Explorer with your helpful suggestions.

And the Reworked Hidden Cities:





I think Hidden City Explorer should be much harder to activate. If you open 5/2, you have a very good chance of getting a Hidden City on your first shuffle. Even if you open 4/3, your chances of getting a Hidden City early are not bad. The hidden Cities cost $9, so they should be something you have to put a lot of work into - something like Magic Lamp.
Another thing: Hidden City Explorer has the awkward problem of being conditionally terminal. Donald made Tournament always give +1 Action so that it never hurts you to play it. With this, though, you're given an annoying, impossible-to-guess decision if you've run out of Actions. Also, Tournament is still a Peddler early on even if you don't connect it. This, though, gives you nothing if you don't connect it, making it very swingy.
I think Machu Picchu's attack is still way too brutal. With Warlord, it's still not too hard to play 5 or even 10 action cards. And the fact that there's only one Machu Picchu just leads to a totally lopsided shutdown of the other player. I know you can block the attack with Fountain of Youth but the odds of that being in your hand aren't great.
I suspect that Atlantis's Province gaining makes it too strong. I would make it "Gain a non-Victory card".
Shangri'La sort of has a problem that trashing is best in the beginning, before you can get this. I know I said earlier that I think these need to be harder to get, but if you want these to be gotten more towards the beginning you'll have to nerf the others. If you want these to be big, powerful cards obtained near the end, though, then I suspect Shangri'La will usually be grudgingly picked up last.
I'm giving all these criticisms because I really like this idea, and I want to see it work.