After an observed 12 years of constant 1g acceleration, you will be 113,000 lightyears from your point of departure, which is enough distance to cross from earth to the opposite side of our galaxy.
Of course, you are now traveling at 99.999999996% of the speed of light. If you actually wanted to stop at the other side of the galaxy to take a look around, you would need to turn around at the halfway point to decelerate, which roughly doubles the travel time.
Acceleration and Deceleration are symmetrical. It takes the same amount of delta-v to accelerate between up to 0.999c as it takes to decelerate all the way back down to 0. Though as you burn fuel your ship gets lighter and the actual energy usage to maintain that constant delta-v of 1G will go down.
As for the energy used to accelerate from 0C to 0.009C compared to 0.99C to 0.999C, I'm not sure. I know the time taken (from an external reference frame) changes, but part of me suspects the total energy stays the same and the difference in time taken is caused entirely by time dilation. However, I suspect I might be messing up reference frames, I don't actually know the equations.
After an observed 12 years of constant 1g acceleration, you will be 113,000 lightyears from your point of departure, which is enough distance to cross from earth to the opposite side of our galaxy.
Of course, you are now traveling at 99.999999996% of the speed of light. If you actually wanted to stop at the other side of the galaxy to take a look around, you would need to turn around at the halfway point to decelerate, which roughly doubles the travel time.