I'm not a physicist, but as I understand it, it takes light 1 year to travel 1 light-year. If the nearest life-bearing planet is hundreds of light-years away,

I'm not a physicist, but as I understand it, it takes light 1 year to travel 1 light-year. If the nearest life-bearing planet is hundreds of light-years away, even if you could travel at the speed of light, it would still take you hundreds of years to get there, from your frame of reference. Time dilation just means it would appear to take even longer from the frame of reference of those you left behind (or those you were headed towards).