You have couple online options for Astoria. Try...
1. craigslist
2. multilisting
MLSLI.com – Long Island Real Estate – Find A Home in Nassau, Suffolk & Queens and you can search for Astoria rentals.
If you don't like those then you always have brokers. Also if you happen to be part of certain ethnicity you can try websites or forums that cater to that group. For example, japanese forum or website like heykorean for koreans.