I'm an avid science fiction reader, but the premise of much of the genre, faster than light interstellar space travel, simply isn't going to happen. Not now, not next year, not a thousand or ten thousand years from now. We aren't even going to have a substantial percentage of the human population outside of Earth orbit 10,000 years from now.
Ironically, one of the most fundamental laws of nature is a speed limit. Nothing can go faster than the speed of light (about 186,000 miles per second). Interstellar distances are frequently measured in units of the time it takes light to go one year. The nearest star to Earth is about three light years away. The Milky Way galaxy is about 100,000 light years across. The countless other galaxies of the universe are all far more distant.
Most of the outs from this, such as the highly curved universe with shortcuts from one part to another in another dimension described in "A Wrinkle In Time", don't work, because there is considerable evidence to indicate that the topology of the real universe is very close to spatially flat. Likewise, even if black holes are ways out of our universe, the tidal effects of the intense gravity of these objects would kill anyone who tried to enter one.
Quantum effects that suggest higher than speed of light possibilities apply on a probablistic basis a single particle at a time. Even if it might be possible to get a single electron to go faster than the speed of light for a few inches or feet, it would be impossible to move a large object a great distance in the same manner. There are some indicatation that information may be able to travel faster than the speed of light through a phenomena inaccurately known as "quantum teleportation", but there are some good reasons to believe that this effect could never even be used to send faster than light messages. While not a true rule of physics, there is a "folk theorem" that holds that communication of ideas at a speed faster than light is impossible.
It isn't just a matter of a speed limit either. The amount of energy needed to get from 20% of the speed of light to 30% of the speed of light is considerably greater than the amount of energy needed to get from 10% of the speed of light to 20% of the speed of light. The best approaches to get to the speed would be hard pressed to get more than a small payload (perhaps a handful of people in statsis or a robotic probate) to even 10% of the speed of light. Even at this speed, you are talking about a 30 year one way trip to the nearest star. Yet, a seed population needs to be considerably larger to create a permanent human presence. Current scientific estimates put the size of the group of people that colonized the Americas at about two hundred. A population large enough to keep medical specialties like neurology functioning at a level sufficient to be medically useful needs to be closer to 100,000. Moving a payload like that on a journal of many light years is a far more daunting challenge.
The solar system presents a different kind of question. It is certainly technologically possible to move reasonable sized payloads to any planet in the solar system on a human time scale. We also know that elements essential to human survival, like water, can be found in many places in the solar system. But, there real question there is whether there will ever be a sufficient motive to move large numbers of people out of Earth and more notably, outside of Earth orbit. My answer is no. Barring an event that makes Earth uninhabitable and puts the very survival of the species in question, or the needs of small groups, perhaps of religious dissenters, to be outside the control of Earth governments and populations, I don't see any reason for more than token scientific and industrial and recreational outposts beyond Earth.
The most common naiive basis for people to colonize the other planets in the solar system is that the Earth becomes overpopulated. But, the Earth is tremendously far from this happening. Earth's population is stablizing (current estimates suggest a speak population in the vicinity of about 10 billion people), as people see that they don't need more than a couple of children in a developed nation where you can count on your children living to adulthood. And, there are vast swaths of the Earth's surface which are virtually uninhabited, yet would be far more favorable for human habitation than any other planet. Siberia, the Australian Outback, North Dakota, the Amazon and Congo Rain forests, the Sahara Desert, the Northwest Territories of Canada, Greenland, Antarctica and the surface of the Oceans all feature a 1 atmosphere air pressure, breathable air, a 24 hour day on average, standard gravitational effects, liquid water than can be obtained more easily than water on say, Mars, and temperatures that, while somewhat extreme, are closer to habitable than on other planet or moon in the solar system. The time it takes to get to any of these locations and the costs of transportation are also far less daunting. In short, even in its current, environmentally degraded state, Earth is a paradise compared to any other place in the solar system.
Earth's population would have to be something like 1,000 billion or more (it is now about 5 billion) before solar system colonization would make any sense, and there is no indication that current population trends are headed there in the next tens of thousands of years. In short, while the prison walls that restrain us are more economic than technological, Earth is also our prison.
The world has gotten smaller and there is no longer a frontier anywhere in the world. What distinguishes our era from one the imperialists of the 16th to early 20th centuries faced, is that the realm of human endeavor now looks far more like a closed system and a finite playing field. When we finally realize this, we are going to have to start being more introspective and more communitarian in our outlook. We can't export our problems anymore. There is one global system for humanity and we have to work within it if we are going to find a path to the good life.