"New York, Washington"
In Korean phonology, the ㅅ is pronounced /s/ (as in English "sand", "sea", "soft") unless it's followed by a /j/ ("y") or /i/ ("ee") sound, in which case it becomes /ɕ/ (similar to English "sh" but with tongue tip curled downward below the bottom teeth). For example (if I understand correctly), 서 is /sa/, 시 is /ɕi/, and 셔 is /ɕja/.
Another way to think of it might be: since there's no huge distinction between those two sounds in the structure of the language, when you're about to put your tongue in position for an /i/ ("ee") sound, it's just more comfortable to let the tip of the tongue stay out of the way and let the blade of the tongue (just behind the tip) do the work of making that articulation. Because of this emphasis on the blade instead of the tip, it comes out sounding slightly different.
(There are even more variations in the pronunciation of ㅅ in other circumstances but I won't go into that here.)
I always struggle with round of questions. Do you put a ㅋ or a ㄱ at the end of New York. Or is it 턴 or 톤 at the end of Washington. Duolingo doesn't seem to really mind either. It just tells me I have a type. But I do wonder if I made these mistakes in real life, would it matter? I mean I guess it doesn't when I speak them because it's going to sound pretty much the same.