What matters most is getting into MBB. NY offices are some of the hardest to get into in the US (other probably being SF). Some countries / regions are harder than others as well btw
Once you are in MBB though, the office doesn't matter anymore -> all else being equal, why make it harder on yourself?
PS: BCG NY does a lot of finance and Healthcare I believe, mostly due to geography. It also works closely w/ BCG NJ. Others may disagree, but I personally don't care that a candidate wanted to join my firm in one location vs. another one. "Why BCG" would therefore be much more important than "Why BCG in NY specifically"