A hard limit like the speed of light doesn't make space travel unfeasible, it makes interstellar travel hard to imagine. There's plenty of reasons to go to space: there are asteroids within our reach that have metal deposits
worth more than the GNP of the USA, there is still much to learn about the threat asteroids pose to the Earth. And don't give me the whole "well send robots" spiel -- humans will always be better able to adapt to the unknown circumstances of new places. If for no other reason than time delays, we should have astronauts on site directing probes.