朝 / 向 / 往 + [direction] + [verb]
朝 / 向 + [person] + [verb]
[noun] + 朝 + [direction]
[verb] + 往 / 向 + [place]
朝, 向 and 往 all mean "towards" and go before the verb. For plain movement in a direction, any of them works.
往 is the usual one for directions. The three part ways when the target is a person, a fixed position or an idea.
往 is about movement to a place, so it can't take a person. 朝 and 向 can.
朝 can describe which way something faces, with no movement at all. 往 can't, and 向 sounds written here.
Learning from, apologising to, asking – a target that isn't physical takes 向 only.
In writing, 往 and 向 can follow a verb of motion, and the destination comes after: 开往上海 "bound for Shanghai", 走向 "walk towards". 朝 doesn't go there.