The ban also applies to sidewalks in the Village Green Park and the Village Housing Authority, New York's WNBC-TV reported.
"It started off with complaints from two businesses that people were standing in front of and the smoke was coming through their doors," Great Neck Mayor Ralph Kreitzman said. "Except for one complaint that we've received it has been uniformly good."
Smokers don't like the new law.
"It's not against the law to smoke. If people don't want to breathe in the smoke ... just don't walk through the crowd of people smoking," said Toni Szilagi.
Trustees approved the Great Neck law Tuesday.
The Tobacco Action Coalition of Long Island, an anti-smoking advocacy group, applauded the ban, Newsday reported.
"Now that the mayor was willing to tackle this problem head-on, and has established precedent, I believe others will follow," Carol Meschkow, a project coordinator for TAC, said in an e-mail.