I think we’ve got another thousand years in this solar system. Once we’ve populated and industrialized our solar system as much as we can, then we’ll be ready do reach for distant stars with people. There are quite a few stars and brown dwarfs within 10 light years.
Even if we never find a way around the light speed problem it doesn’t mean we can’t go, we just wouldn’t be able to do it at light speed. Within 1000 years we’ll probably be able to keep people in stasis for long periods. In 1000 years we’ll be able to achieve a considerable percentage of light speed. In 1000 years we’ll be able to build the really big ships we need. In fact we will probably do all of those things much sooner than 1000 years from now but I doubt we’ll be try to send men beyond our solar system for at least 1000 years.
1000 years is probably optimistic, given that it has been over 45 years since we first landed a man on the moon (a feat that still no other country has managed) and it will likely be at least another 50 years (probably closer to 100) before we land anyone on Mars.
In his novel 2312, science fiction writer Kim Stanley Robinson describes using hollowed-out asteroids, roughly 9 kilometers in length as "terrariums" powered by engines and containing fully self-sufficient towns and thousands of occupants inside them for the real long hauls.
So if we can put people in hibernation for 1000 years, how will that effect them psychologically when they wake up and all their family and friends have been dead for 900+ years. Maybe earth society will have advance so much that people will see them as aliens. Maybe earth society will have advanced so much that their journey was merely scientific masturbation and blowing a lot of resources. What do people now remember from 1000 years ago?