Assuming the need is due to a catastrophe with Earth and not the Sun, why leave the solar system? If we can build a ship with resources that lasts generations,

Assuming the need is due to a catastrophe with Earth and not the Sun, why leave the solar system? If we can build a ship with resources that lasts generations, park it in Earth's (or another Sol planet's) L4 or L5. Going in search of another star seems foolish.