While I admire Hawking using his celebrity to promote a noble cause, his thought process doesn't quite point to "genius" on this one right now.
None of the other planets in human-survivable range (without anything from Area 51) have breathable atmosphere, so we'd have to build closed systems to sustain us on other planetary bodies.
So, why not just build an underground Arcology right here on Earth instead and save the travel time ? Unless the Earth actually explodes, it should be able to sustain a community just as well as any on another planet... as long as it has strong doors and locks.