In talking about physical/geographical directions, I'm pretty comfortable using 朝 and 向 and 往 for the meaning of "to" or "toward". But I would be hard put to describe to a Chinese language learner any differences in usage or meaning among these three words. Are there any important differences?
See the Chinese Grammar Wiki. The explanation is quite extensive with many examples.
Some relevant parts:
向 and 往 can be placed after the verb, however it has to be used with an appropriate verb, Often used verbs are 开, 飞, 发, 运, 送, 寄, 带, 驶 etc. As you can see, this are words that at least imply some sort of motion. In addition, compared to 向, 往 is used more often with those verbs, because 往 expresses the destination while 向 merely expresses a direction, 朝 cannot be used this way.
When the action that takes place is specified to a specific target, use 向 or 朝. 往 cannot be used this way. Also, when the verb is a concrete action, the use of 向 and 朝 are the same, and they can be interchanged.
When the verb has an abstract meaning, you can only use 向, and you cannot use 朝.