It is amazing to find pockets where General Relativity has not penetrated at all.

It will certainly take >100 years for the people left behind. On board it could take time anywhere between infinity and zero. Too long, though, and they wouldn't go.

That's not true. If you travel close enough to the speed of light time dilation becomes so extreme that it may only take a few subjective years for the travelers to travel 100ly.

As your ship approaches c the distance to your destination gets physically shorter due to length contraction.