In a fantasy world where dragons exist, you meet an old woman who saw where the dragon, which some time ago attacked a nearby village, went about ten minutes ago. You ask her, "Did you see where the dragon went (the line isn't mine, from a computer game in the same situation) ?", can she answer with "It went towards Riften (a city in the south)" even though she doesn't know if the dragon has reached the city yet(it's a long way) and even if it will actually ever reach it? If "It went towards Riften" isn't good, does "It set off to Riften" better?
"It went towards Riften" is good. It simply describes the dragon's direction of travel (something that the old woman could observe). It does not imply that the dragon has arrived, nor that it will ever arrive. It does not say anything about the dragon's intentions, desires, hopes or plans.
"It set off to Riften" is worse. It implies that the dragon intends to travel to Riften. Unless the old woman has been talking to the dragon about its future plans, how could she know what the dragon intends?