It seems likely that mankind, and aliens who got started before us, will eventually establish permanent residences off of their home planets. In the not-so-distant future, the majority of mankind, by percentage, will live off-Earth. However, you should think of the planets as being the bottom of very deep holes, with most of them being too hot, cold, poisonous, exposed to radiation, or too much or too little pressure. The task of getting and leaving these places is risky and expensive, too. Let's just give up on the idea of colonizing Mars for the forseeable future, please! It may not always be so, but the solar system's orbital rocks are easier resources to get, and spitting up material from low-gravity objects with mass drivers. There's no point to terraforming a planet when that will take thousands of years, and no human civillization can keep a project like that, and it's cash flow, going for so long.
In short, we're just not gonna live like pale, stick-figure trolls in underground caverns on the moon or mars. Mining will be done by pulling a big bag over an asteroid and breaking it up from the outside in. Attached refining equipment will separate useful elements and chemicals. This will be mostly-automated. We'll use the tailings as concrete to build our colonies. A gigantic mirror will heat the crushed rock and sinter it into shape, like an enormous 3d printer. There is enough material to build millions of them in OUR OWN solar system, and they'll be essentially self-sustaining once they've been established. Conditions inside will be perfect for human life. It's a far better prospect than making do with low-gravity moons and poisonous planetary atmospheres. Groups of colonies might form "countries" and others will operate independently. The colonies will be built robotically, so the cost will eventually drop to the point where one might be owned by a single family or other social group.
While most colonies will participate in a humanity-wide economic and social network, a life of physical isolation and self-sufficiency will be the norm for most. We'll be in communication, but not often physically visiting other colonies. Some of these may try hurtling themselves onward to the next closest star. They'll stay in touch the whole time, they'll just be permanently out of reach from then on.
The stars DO NOT need to be sun-like, nor do they need Earth-like worlds! They just need to have exploitable resources in easy reach. Red and brown dwarfs are more plentiful than any other type, and they'll last orders of magnitude longer, too. This is probably where the majority of intelligent life will live at some point. Not to miss out on any exploitable resource, those who live around dwarf stars will push onward to practically every type of star within reach. A million years or so, and we'll have colonies throughout the galaxy, and hundreds of alien neighbors to enrich our culture and science.