If you go to something like Trappist (40 ly) at 0.01c (very optimistic), it's not just that everyone you know will be dead when you arrive. Your entire nation will have disappeared to the sands of time. The landfall announcement you send back will be incomprehensible because of language shifts, and you won't live to see the reply. Meanwhile, such a trip would be an enormous investment, requiring multiple nations to bankrupt themselves, with no hope of even surviving to see the outcome.
With that, it's very hard to imagine interstellar travel being feasible with our current understanding. There would have to be something like FTL travel or wormhole. The only "realistic" development, (much) better engines that can do 0.1c, would not actually change much.