Other possible issues in the question: Is biking also an option? What do you want to do at the carwash when you get there, wash the car or buy a bucket, sponge, and soap? Is the car already at the carwash and you want to drive a second car? What about calling the carwash to see if they will have someone wash the car for you?
There are many ways to interpret the question because it contains ambiguities that must be resolved through assumptions. (Lacking information and constraints such as possible alternatives that satisfy the goal of washing the car.) The follow up questions I asked also have assumed answers but answering them provides no clear resolution to the ambiguity present in the original question.
So, no, I disagree that there is any solid implication of where the car is. And even if there is a solid implication, it can hardly be reasoned that it "isn't an XY problem" or that the question is clear cut in any real sense.
Doesn't offering two options to the LLM, "walk," or "drive," imply that either can be chosen?
So, surely the implication of the question is that the car is where you are?