I could see someone saying they were "at the sink" if they were working in the kitchen in general and their hands were wet or had food on them, so they didn't want to go handle something else (as in, to open the door, answer the phone, break up a sibling squabble), but I've never heard of the term "sink" being generalized to the counter around it in common usage.


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I've never heard anyone say "to home, but then I've never been to New England (I did live in eastern Pennsylvania as a child, twenty-five years ago, but I don't recall hearing it and apparently my parents never picked it up if they heard it). It's definitely not generalized throughout the United States.