Er, I'm not quite sure about that. First off you don't mention any necessities; how are you going to feed an entire city in space? Scrap that; where's the oxygen going to come from? If the answer to both those questions is gardens, likely 75%+ of the ship will need to be nothing but plants. Also, for any long-term mission like the one you're describing, it becomes imperative that we find some source of artificial gravity. And electricity? If you're going outside the bounds of our solar system, then solar power might not be reliable.
2 lightyears would be 20 years away if we built an Orion spacecraft. These are about the size of a city so living on one shouldn't be an issue even without hibernation. Plus you have to factor in time dilation due to traveling at 10% the speed of light. In all, reaching a planet that far away is perfectly within our grasp if we were to do so with the intent of settling there. We have the technology, we just don't have the interest.