It's one hundred percent correct. The verb does not have to agree with "lots" (which is technically plural) but with the noun modified (the true subject). The full sentence might be "There's lots of stuff to do in New York." "Lot's of" is not the subject, but is merely serving as a modifier.
Other examples: "There's a lot of beer," "There's lots of beer," "There's much beer." All three have the exact same meaning, so all three are in the singular. (Although the use of "much" in affirmative statements is a bit unusual in contemporary English.) "Lots of" is not the subject; it is just a modifier for "beer," the real subject. In your examples, the real subject is "stuff," not "lots."
By the way.. is this a line from a classic Broadway musical?