FORGET PLAN B. We will either survive under plan A or we will die. Which, by the way, would not stop the world spinning.
Problems to overcome with Plan B (living somewhere else)
1 Energy
Before we can live in cities orbiting the earth, we have to lift a tremendous amount of weight. Whether we do this with rockets or a space elevator (one end anchored to the earth, the other end anchored to a platform orbiting the earth), a great deal of matter and energy is involved. A lot of fuel is required to boost rockets into orbit (even when they are carrying nothing).
The space elevator is not energy free either. Mass still has to be pushed or pulled away from the earth using a very very thick cable. (The cable has to be thick to hold itself together, before it can carry anything). There probably isn't any form of matter that won't end up being quite a lot of weight to manufacture.
2. Radiation
Once in space, animals, plants, and materiel will be bathed in penetrating visible, solar, and cosmic radiation. There are means to block radiation, but again -- cost.
3. Time
No matter how fast we go, (and the fastest we are likely to go is a very small fraction of SoL) it will take us a very long time to get to anywhere that offers a viable environment for humans, animals, and the plants we depend on. (And this assumes we know where that is at the start of the trip.)
So, whatcha gonna do? Hibernate for 50 years; wake up; leap out of the hibernation box, and suddenly go to work? I don't think so. Live inside a large hollowed out asteroid? Travel in a FTL space ship like the Enterprise with inertial dampeners, detachable saucers, dilithium crystals, et al?
It's possible that we could live inside a large hollowed out asteroid for 60 years, but... doubtful. Remember, we will be voyaging in space as the prickly, somewhat unstable, quite often maladaptive, argumentative, emotion driven primates that we are, and that describes the cream of the crop. I can't imagine a cage of 150 humans locked up together for 60 years with NO EXIT and being either bored out of their minds or suffering repeated crises--some external, most internal--ending up ready to found the EARTH II civilization.