Interstellar flight alone is not of interest. OTOH, it would allow earthlings to become visitors.
Commerce. If we use our experience as a basis here, this is the #1 interest that would lure alien explorers to this neck of the woods. Commerce is what got us to cross the Atlantic: looking for routes, buyers, suppliers, riches and land. All science-first approach ("they should come to study us") is so 20th century utopism.
But without really being sure what matters to aliens the most, commerce, tourism or science, makes it hard to lure them. We sent Voyager with curiosity in mind: songs, poems, language samples, pictures... But we could have sent instead a list/sample of our prime minerals, water supplies, preferred payment methods and our "1-800 number" for contact. Scientists can be so un-enterpreneurial sometimes!
Now, what then could get their attention and provoke a visit?
Become a menace.
Without really being sure what matters to aliens makes it tough to envision a way to get them really interested on the 3rd rock enough to launch a mission or send signals. So the most effective (and reckless...) is to become a menace, or at least a nuisance, to them. Fiction has played around with that idea, nuclear capability being the trigger that got them to notice or outraged enough to wipe us out...
Let's say we develop a gravitational wave cannon capable of making Sirius shoot over as a billiard ball into Procyon. Oh, now that would get their attention!