Obviously his best known contribution to the human experience was traveling to the nearest large astronomical body, and that landing will be historic forever. His friend and the second person on the Moon with Armstrong, Buzz Aldrin, also has great remarks. President Obama also made a statement.
He obviously helped the sciences move forward, paving the way to more missions to the Moon and bringing back and leaving materials to better study the body and thus the rest of the solar system. Armstrong also did some teaching after his historic mission at the University of Cincinnati for about a decade.
When it comes to skepticism, he wasn’t so involved in debunking the Moon landing hoax, (Buzz did a lot of that, including punching one guy in the face), but Armstrong did take part of an expedition to Cueva de los Tayos which showed Erich von Däniken was dishonest, thus also helping kill the ancient astronaut hypothesis.
He will obviously be missed, but his efforts and adventures will live on as long as humanity exists.