You can't just jump to the speed of light. You need to accelerate large amounts of mass to 99% the speed of light - it takes INCREDIBLE amounts of energy (E=MC^2 and we know what a large number C is).
Currently, the slowest form of propulsion, and the most fuel-efficient, is the ion engine. For the first half of your journey you would be pressed into your seat by acceleration, then the second half you would be turned around and pressed into your seat by deceleration. I guess we would probably need to be unconscious.
Proxima Centauri is the nearest star, and it is ONLY 4.24 light years away.
In short, at a maximum velocity of 56,000 km/h, you would take over 81,000 years to traverse the 4.24 light years between Earth and Proxima Centauri. To put that time-scale into perspective, that would be over 2,700 human generations.
Our Galaxy is 980,000 light years across. :/