Sirius, our CLOSEST neighbour is 8.6 light years away, or 86 trillion kilometres, or 5,879,000,000,000 miles
lets assume einstein was right, and that travelling faster than speed of light is impossible.
so if they have travelled at 99.9% of light speed - took them 8.6 years.
remember, you want to go as fast as you possibly can - there are HUMANS IN THE DEEP FREEZE (according to the intro) who might not want to pass their 'sell by date'. The reason why they were in cryogenic stasis was to make the ship as compact as possible - very important when slinging something across the universe - to all intents and purposes the ship becomes a light-speed torpedo.... which can get destroyed/shot off course by colliding with a rock the size of a grain of sand.
if they travelled at half light speed - 17 years. If you can freeze a man for 8 years, 17 is not to much of a stretch.
After 100 years, you get problems. The humans that were awake shuffle off this mortal coil, and if the succeeding generation of technicians miss out an important step..... oops!
Furthermore, cars have trouble lasting 25 years.... fridges last about 10. Don't think i would trust zanussi to make my people-fridge.
propulsion is another problem - we need something that will push the ship along without the fuel taking up all the room on board.
Navigating is important. Step up to pluto, and the whole constellation changes. the computing power required to calculate all of this at the speed of light would be tremendous.
now, you've gotten your ship to light speed, and the electronic abacus is ticking away quietly. How do you stop the ship when you get to sirius? slingshot Sirius B?
One solution to these problems is generational ships, where you get on and your Childrens' children get off. these have tecnical problems, such as food production and waste disposal, becoming in effect self-supporting cities, but dont have the propulsion problems (interstellar hydrogen, solar sails) navigation problems (space is big... lots o time to do the maths) and slowing down problems are solved as your really not in a rush. But firing off generational ships when the enemy is on your neck is pointless - they'd just get popped immediately.
Happily, the point is moot. We're stuck on this rock. We're hemmed in by the asteroid belt, the kuiper belt and the Oort sphere. Attempting light speed through that lot would be like trying to run through a blender (humanity, does it blend?). The solution? Hyperspace. We'd need to be able to create a worm hole from where we are, to where we want to go in order to get off this rock that we have polluted with our industry. Ironically, it is industry that will be creating the computers that the scientists work the answers out on to the problems created by industrialisation.
As such, hyperspace would take no time at all.
So, to answer your question - from present day to a point in the future where we can manipulate space-time. Large hadron collider anyone?
