Oh, yeah, forgot to add that. I you definitely want to do LQG, you should apply to Perimeter Institute. They also have a very strong string theory group, so, you would get a good idea of what's going on in both approaches. The thing is that if you apply directly to PI, they will most likely accept you to work within a specific group, so, it might be harder to change fields. But you could also apply to the University of Waterloo and get a supervisor at PI. For stringy research, I would suggest going to either UCSB or Stanford over PI, simply because they have larger groups.