National Astronomy Day is aimed at connecting the public to astronomers and astronomy enthusiasts. It was started by Doug Berger, the president of the Astronomical Association of Northern California in 1973. He had the idea to set up various telescopes in busy urban locations so that passersby could enjoys views of the stars. His idea took off and the event has grown to include several sponsoring organizations associated with astronomy.
Astronomy Day changes every year based appropriately on the first quarter moon, which is generally between mid-April and mid-May. Check with you local science museum or planetarium to see if they have any special events to celebrate National Astronomy Day!