Comparing 朝 vs. 向 vs. 往
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.