Climate refugees are going to be the big issue, not where to choose to move if you have that freedom. Any question of where to go has to somehow answer "What happens when everyone else who can tries to go there?"
Can you really keep out tens of millions of people with a wall? Absolutely, if you're willing to enforce it. You may have to kill some of those people to do so, though. Which puts us right back at your second paragraph.
Europe and the US kept hundreds of thousands of Jewish refugees out of their countries during the Holocaust. We certainly can do it again, with just as shameful results.