Hmm. I need to know more about this destination thing.

Presumably at the start of the game you don't have any destination, so you need to see at least two destination cards for the mechanic to matter. And indeed they have to be different ones due to the "another". Will there be enough lands with expedition for that to occur? I'm thinking you'd need more than five commons and five uncommons for that, but maybe I'm wrong.

Hmm... also, suppose I have a deck with 4 of these and 4 Hidden Waterfall. I play one of these and name Hidden Waterfall. Then I draw one of these. I fear in that circumstance players might be tempted to avoid playing the second copy of this, which is going to stunt their mana development.

I only did a very quick playtest some time ago just to check if it the mechanic works as intended (it seems it does) but I don't know enough yet to answer your concerns. The "another" clause is for flavor (seems kinda silly you're on location A and your next destination is...A again) but it can be dropped for gameplay's sake.

Do you think this might look better as a keyword and something keying off that keyword?

"Expedition (When this enters the battlefield, name a land as your destination.)

When Royal Palace enters the battlefield, if it was already your destination, tap up to three target creatures."

For Constructed purposes, it's probably better to have "another" so that decks don't just play one 4x set of Expedition lands and no others.