Beyond the Doylist explanation that GRRM wanted to introduce his readers to as much of his setting as soon as possible and the simplest way to do this is to have the characters go on a road trip, why would Robert and his entourage travel to Winterfell and back by land rather than sailing to up the White Knife and back via White Harbour like Cat later did?

Well, keep in mind Robert’s objective wasn’t to travel to Winterfell as fast as possible. Instead, Robert’s trip to Winterfell was a royal progress, where the point is to dazzle your subjects with the splendor of the king’s person, to dispense justice and renew the social contract, to renew the personal connections between the nobility and the monarch, and occasionally to gently bankrupt the politically suspect nobles by making them pay for everything.

In this case, it’s a good opportunity for Robert to show himself to the Riverlanders, both the ones who supported him during the Rebellion, and the ones who didn’t. There is a reason he stays at Castle Darry.