The problem with space travel is that of propulsion. One has to literally throw stuff out of the back of the ship to accelerate. Basically, give that stuff momentum in one direction, and the ship will gain momentum in the other (so that the total momentum stays zero). This means that you have to carry a bunch of stuff (propellant) with you to throw out the back. And as you accelerate, you have to accelerate the propellant too. Its all horribly wasteful and it means that you cannot sustain acceleration for long periods of time.
What if you could sustain acceleration for long periods of time?
The results are surprising.
At a comfortable acceleration of 1g, you could get to:
The Moon in 4 hours
Mars in 2 – 5 days
Jupiter in 6 – 7 days
That is by accelerating up to the halfway point and then decelerating.
We could literally colonize the solar system and traverse it easier than ships traversed the Atlantic Ocean in the 18th and 19th centuries.
If you could sustain this even longer, you could reach relativistic speeds. The universe then becomes your playground.
At a mild 1g you could travel to:
Alpha Centauri (4.3 LY) in 3.56 years!
Tau Ceti (11.9 LY) in 5.14 years!
Betelgeuse (309 LY) in 11.18 years!
Galactic Center (30,000 LY) in 20 years!
Now, mind you that relative to the Earth, your time is slowed down and it will take 30,002 years for you to get to galactic center. But you would make it!
A civilization that enjoyed this kind of travel would have to become nomadic.
What if you could accelerate at 10g?
Galactic Center could be reached in 2.45 years!
The other side of the galaxy (150,000 LY) in 2.76 years!
The Andromeda Galaxy (2,000,000 LY) in 3.26 years!
And if you could accelerate at 25g (the accelerations typical of the purported UFO that followed JAL 1628 across Alaska in 1986)?
Galactic Center could be reached in 1.05 years!
The other side of the galaxy (150,000 LY) in 1.17 years!
The Andromeda Galazy (2,000,000 LY) in 1.37 years!
If such a thing were possible, real interstellar space travel would become an engineering problem and a species could literally spread across the galaxy or even to other galaxies.
For more distances and times, check out the Relativistic Star Ship Calculator.