This advice comes from a REAL GREEK friend -
"The only way, really, to enjoy authentic souvlaki is to eat it in the street, specifically at the corner of Ditmars Blvd. and 33rd Street in Astoria. Right in front of Thessalonika Jewelers is where you will find Elpida and her most succulent souvlakia (souvlaki stand). If you want a sit-down experience, the best one would be Tony Souvlaki - on 31st Street between Newtown Avenue and 30th Avenue, right under the El. Not expensive, very tasty, very clean."
Hope that helps - Dena