So there are no other planets like Earth out there?

None close. The nearest one is 4.25 light years away. That's far enough away that adult humans won't be able to reach it using any propulsion system consistent with the laws of physics as we know it now before they age out of child-bearing years. Which means having kids on board - a colonization ark. Which means all the problems of physiology and psychology that make such an endeavor all-but-impossible to achieve.

Technology advances.

It's not a technology problem, though. It's a problem of biology, ethics, psychology, and economics/return on investment. We don't know what happens to babies and children if they have to grow up in an environment with significantly less than earth-normal gravity, lots of reasons to think it would be bad, and no ethical way to find out if it's safe. We know that most humans are not psychologically equipped to deal with long periods in confined spaces in close quarters with other people (which is why the Navy screens for the ones who are). And while there's plenty of economic reasons to explore space, there aren't any reasons to colonize it. Same dynamic as research in inhospitable areas on earth; there's plenty of reasons to do undersea research, but no incentive (economic or otherwise) to set up an undersea colony where people live for the rest of their lives and raise families.

We can see how it might be possible for technology to advance to the point where we can safely send adult humans to another planet for research and exploration. Or to establish a permanent research facility that adults travel to for long periods of time, like we have in Antarctica. But there's no real path forward for a human colony, which will (by necessity) involve babies and kids and lots of people that neither chose to be in that environment nor have any useful skills to contribute to that environment.