Have an interview with the BCG NY office- what sets apart the BCG NY office from others?

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"

The honest answer is that MBB firms in New York are relatively similar. If you compare offices across the firms, New York, San Francisco and London have the reputation to be a bit tougher when it comes to recruiting talent (--> supply and demand). 
If I were you, I would think about a functional or industry area you are genuinely interested in and could imagine specializing in a few years down the road. Research NY BCG partners that have released thought leadership pieces (e.g. articles, research papers, etc.) in this area and mention them in your interview - it shows that you have done your research and can clearly identify differentiating factors across MBB