There is a man and a woman standing nearby the drugstore.
There are a man and a woman standing nearby the drugstore.
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Strictly speaking, according to grammarians, it would have to be the latter, "There are a man and a woman standing near [more idiomatic than "nearby"] the drugstore."
The man and the woman are standing there. There they are. There are a man and a woman near the drugstore.
But, you will frequently hear, "There is," in that situation. People say it a lot. It really doesn't even sound wrong to me, and I say it that way myself sometimes.
So if the population says it, is it really incorrect? I say either is acceptable, but only your second option follows the rules of English grammar.