Well theoretically, it is possible for us to travel to the distant stars and planets within human timescales or even near-instantly but there's a whole lot of advanced technology we would have to develop first. As you say, going the familiar route of a fast spaceship would take far too long...multi-generational trips with no way of knowing exactly whether a distant planet could support life.
Traveling faster than light may be possible but not in the way most people think of it. Scientists have already exceeded the speed of light in lab experiments with particles which may lead to quantum computers much faster than current designs...it's also thought that in the next few decades, we may have smaller and faster computers that exceed the capacity of the human brain.
There is also a concept in quantum physics called quantum entanglement or superposition whereby two particles separated in space act the same way. So theoretically, if you could clone or disassemble yourself and your brain at the atomic or sub-atomic level and reassemble that clone on a distant planet using QP principles, in theory, a "person" could travel to anywhere in the universe although there are also metaphysical considerations of whether a "person" is more than just an assemblage of atoms. Our bodies and brains are basically made up of atoms which in turn are made up of smaller sub-atomic particles which act in strange ways due to principles in quantum physics. If we get to a point in the future where we can manipulate those principles of QP, we could in theory replicate or "transport" ourselves to distant Earth-like? planets....no space travel in spaceships necessary...quantum physics allows for an instantaneous connection between two quantum particles in space.
It's called quantum teleportation by some....similar to the transporter mechanism shown in Star Trek which disassembles the atoms in the bodies or objects and transports them to a planet or other spaceship, etc.. then reassembles them correctly.
http://en.wikipedia.org/wiki/Quantum_teleportation
Conventional space travel poses serious problems and limitations due to particles in space...traveling at even 1/10th the speed of light would obliterate a spaceship by striking a small dust particle in space which is filled with them. E=MC2 prevents near-lightspeed travel in conventional means ....contrary to what Star Trek and Star Wars-type movies show. Wormholes are another hypothetical possibility although how much energy would be required is a limitation. If we ever develop the means to turn ordinary matter directly into energy, it could offer huge potential energy sources to do so. The matter contained in a single medium size tree has enough potential energy equivalent to power the whole US for 11 years due to the E=MC2 mass-energy equivalent formula. Nuclear weapons and reactors are the closest we have so far but they rely on unstable nuclear materials. The question would be whether such a machine or method would destroy itself in the process....how would you contain the matter being converted into energy? If any matter could be converted, would that include the machine itself?
M - E conversion....
"So one gram of mass is equivalent to the following amounts of energy:
89.9 terajoules
25.0 million kilowatt-hours (≈25 GW·h)
21.5 billion kilocalories (≈21 Tcal) [9]
21.5 kilotons of TNT-equivalent energy (≈21 kt) [9]
85.2 billion BTUs[9]
568,000 US gallons of automotive gasoline"
An ordinary pencil weighs around 10 grams...do the math and one pencil could power your car for 284,000 miles at 20 mpg M-E equivalent. Now THAT would be a fuel-efficient car!
http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
This might all sound far-fetched but a hundred years ago, we were driving around in Model T Fords and riding horses...heating homes with wood and coal and 50 years before that lighting our homes with whale oil. Who can say what the next hundred years will bring...if we survive it would be another issue.