Throughout the first two series of Sherlock, Mycroft sends a car to pick John up and bring him to him. Just about every time, they meet at a different location. He doesn't seem to have any issues with protecting his identity (once his identity is revealed). His only concern, and it is only an occasional one, is to prevent Sherlock from being aware of the meeting or what is being discussed.
Why does Mycroft meet John in different locations?
I do not any official sources to base this on but I assumed that the random odd meeting places was for safety and privacy.
Privacy: It is unlikely that anyone would blunder passed without being noticed. No one has a reason to stay within microphone eavesdropping range (like they would in a pub). Mycroft might not even want his colleagues to hear what was between him and Holmes, people in his position trust as few people as they possibly can.
Security: It would be very hard to predict where they were going to meet so anyone with any sinister motives would have their work cut out for them to interupt the meeting or do anything to Mycroft. Even John did not know where the meeting was until it had started.
Firstly, to keep the meeting from prying eyes and ears, mostly Sherlock. But as a government official anything he says could be important to a lot of people. So one reason is to keep secrets.
Second is that both of the Holmes brothers have an obvious flair for the dramatic, made obvious by the way Mycroft talks and the way Sherlock acts.
