"Do you know the way?"
I am a beginner in Chinese but I don't think the chinese phrase is wrong. I got the impresion "renshi" = being familiar with someone or something. So when you want to ask "do you know the way" you actually ask if you are familiar with that specific itinerary.
On the other hand "zhidao" means literaly to know something as in a specific information. So if you want to use "zhidao" you should say something like "do you know how to go [somewhere]". To me "ni zhidao lu ma" sounds as if you ask the other person if they know the meaning of the word "lu".
This is just a guess of mine. Please, anyone fluent in Chinese, verify it or correct me.