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I've heard DC firms want to see ties or a reason to come to DC, whereas NY firms of course don't care about ties. However, does anyone have past experience of a backfire occurring because a student emphasizes DC ties to the DC office of firm X, which office then tells its NY branch of student's DC ties, undermining said student's shot at NY office because the NY office thinks the student will go to DC?

I interviewed for both the NY office and the DC office of my firm and I think I overthought this. Just tell both that you are extremely interested in the firm as a whole, and in particular the office in _ city appeals to you because of xyz. I don't think they will ask you to express a preference but if they do just weasel out of the question. (e.g., "That would be a tough decision," etc.).

Having seen my firm recruit law students who split their summer between the offices, I don't think it particularly hurt them either way. Either office would have been glad to take them. For the smaller office, you may want to give them a bit of extra encouragement that you actually would love to live there if you were given an offer.