People may accuse me of being pedantic, but I don't like either of them. You should say "May I ask what your destination is?"
The answer might be Shanghai, for example.
One does hear "where" used when somebody wants to know your destination, but in my opinion the usage is loose and illogical. In the example above, "May I ask where your destination is?" could perfectly correctly be answered by "My destination is in northeastern China."
- For Teachers