Word/phrase/idiom to describe avoiding answering a question by stating the question doesn't need to be asked

One relevant term from logic:

red herring — The idiom "red herring" is used to refer to something that misleads or distracts from the relevant or important issue.

Specific forms of red herring exist and I find that appeal to motive fits nicely:

appeal to motive — Appeal to motive is a pattern of argument which consists in challenging a thesis by calling into question the motives of its proposer. It can be considered as a special case of the ad hominem circumstantial argument. As such, this type of argument may be an informal fallacy.

The person who answers that you should go to Burger King instead is assuming that your motive for asking the question is that you want to get something to eat. This is an invalid assumption and, therefore, their answer is completely irrelevant.

More informally, this pattern of behavior is simply known as "dodging the question":

dodging the question — Question dodging is the intentional avoidance of answering a question.

On that wiki page they have a list of example forms and these seem particularly apt. In response to the question, "Why are you here?":

• Answering things that weren't asked ("I'm in the corridor.")
• Questioning the question ("Are you sure that's relevant?")
• Challenging the question ("You assume I am here for a reason.")
• Giving an answer in the wrong context ("Because I was born.")

The motive for dodging the question in your example is that they don't know the answer. Thus, they answer a different question.

You might consider this as a case of ignoratio elenchi, where an irrelevant argument is presented as an answer to the question at hand:

Ignoratio elenchi, also known as irrelevant conclusion, is the informal fallacy of presenting an argument that may or may not be logically valid, but fails nonetheless to address the issue in question.

[...] The nature of the fallacy, then, consists in substituting for a certain issue another which is more or less closely related to it, and arguing the substituted issue.

It seems a little grandiose for what you're describing but is a good fit nevertheless.

I'm not entirely sure that this is the word you're looking for, but it's a good place to start:

non sequitur

Look under the section called In everyday speech.

The response in you post doesn't prerfectly qualify as a non sequitur, though, because there actually is some connection to the original question.

The link points to a concept called derailment that seems to be a cognitive problem, but the word fits well in this context. To derail a conversation means to interrupt it so that it goes off topic.

The main thing which the person has done is not some technical manipulation of a question; this person has tried steer the conversation to his favorite topic -- himself, and his opinions and preferences -- by dropping a shift response. There doesn't seem to be a glib word or phrase for "attempt to steer conversation toward oneself", though. In general, using one topic as a springboard into another one is a segue. That coworker used your topic about how to get to McDonald's to segue into opining about his or her preference for Burger King.

Someone who steers conversation toward himself (specifically, his superior wit and better grasp of the "bigger picture") by constantly looking for the "real problem" that someone is trying to solve, and offering supposedly superior alternatives which avoid the specific question, is a "smart ass" or "smart alec". The latter can be used as a verb: "smart alecing/alecking".