We aren’t going to travel to other star systems for a long, long time. If ever.
However, we’ll be bringing other star systems to us. There are already plans in NASA for telescopes large enough to image earth-like planets around other stars. Later plans include telescopes so large that they will be able to spot large artificial structures on planets around other stars.
Space interferometry is what allows this to happen. A single telescope like the Hubble has a mirror about 2.4 meters in size. The NGST, due to fly in about 8 years, will be slightly more than triple that size. But with interferometry, you can fly arrays of telescopes and make them look like one big telescope. One plan is to have an interferometry telescope with a theoretical aperture of about 6000 kilometers!
Within 15 years, we should be flying the Terrestrial Planet Finder, which will be able to analyze atmospheres of earth-like planets around other stars, including biological signatures indicating life.
The most advanced mission that NASA is already planning for is the Planet Imager, which would use a large array of NGST-like telescope and interferometry to actually image continents and oceans and other features on earth-like planets orbiting other stars. We’re not really close to this thing yet - it might be 30-50 years away unless NASA gets significantly more funding.
This program could be extended almost infinitely - imagine a telescope with an effective aperture the size of the Earth’s orbit…
Clearly, there is an awful lot of exploration of other star systems we can do right here in Earth orbit. The really interesting question is, what would we do if we looked at a star system with a huge telescope, and saw evidence of an advanced civilization? What kind of pressure would arise to go there?
Realistically, we can imagine the next steps - we’d probably start planning bigger telescopes to see more and more of that civilization. We’d aim huge radio telescopes at it to attempt to pick up signals. We might even try to communicate with them by firing large lasers at it or something.
But it’s all going to depend on what we find out there, and we’ll probably have a good idea in our lifetimes. We’ll have mapped the planetary systems of maybe the nearest 100 stars in our lifetimes, knowing which ones have atmospheres, what those atmospheres consist of, etc.
There are theories suggesting that the Earth is extremely rare. Current studies of other star systems have shown two types of system - ones with Jupiter-like planets that are extremely close to the star, and ones with huge Jupiter-like planets much farther out, but in highly elliptical orbits. Neither type of solar system is conducive to having an earth-like planet in orbit in the ‘habitable zone’ of the star, because the orbits would not be stable.
Other theories have suggested that life won’t develop at all in solar systems that don’t have a large Jupiter-like planet in the outer system, because these planets act like cosmic vacuum cleaners preventing a high rate of bombardment of meteors in the inner system.
We should have answers to these important questions in the next two decades, and those answers are going to give us a much greater understanding of what else and who else may be out there.