It would probably take us MILLIONS of years to reach the nearest planet that's even remotely habitable.
That's assuming we use the present technology of "one short blast of acceleration followed by drifting forever". We would no more do that than Columbus paddled a canoe to cross the Atlantic.
A constant 1 g acceleration would reduce travel time considerably, plus it is needed to keep a human's bones from turning to mush over many years.
(A spinning cylinder with 1 g on the inside has its own issues, beside the long travel time, baring a "huge" engine plus fuel supply for that acceleration. It has to be "really big" so the inside surface area is enough live on comfortably. A very small cylinder spinning fast would have so much coriolis force that it would probably knock you over every time you stood up.)
Granted it will also take a generation ship (or suspended animation, or genetic manipulation for longevity) even if the time is down to hundreds or a few thousand years. Add on the other things needed to survive a long, one way trip:
100% recycling efficiency (both biological for food and material to replace old equipment)
failure proof power sources other than sunlight
sufficient medical supplies to treat cancers, mutated germs, and psychological illnesses
ways to create new entertainment (everyone would go crazy-bored being stranded on that "desert island" with only a favorite eBook, DVD, or iTune)
manufacturing facilities (to replace the iPads and LED lighting that will eventually break or fail)
research facilities (will your children's children's... be better off than you when you left town?).
Finally, colonists can't expect to find friendly natives to help them build houses, or bio-fuels to run the factories and transports, so it all has to be brought with them, or nano-fabricated at the end of the road. Plus, regrow those genetic stores of Earth's biosphere. (I'd be wanting to check if that 300 year old myth about latte or tea with cream and sugar tastes as good as the eBooks mentioned.)
Whether humanity even goes anywhere in the near term, i.e. 100-200 years, these are just the technologies that should be developing here on Earth. An active space program might just make them happen faster, with less built-in obsolescence.