The Beta NYPD color sheme, the Brooklyn Bridge/Boutoug 59th street bridge (Callahan Bridge), the elevated subway in Queens (especially Portland being a mix which ressembles Bronx, Brooklyn & Queens a lot), Broadway, Center park, West-Bank building, Overlaping Expressway at Staunton (which strongly ressembles to the one on the posted pic), Shoreside Vale heavily based on the suburbs in Long Island, New Jersey, Hackensack, all the ladders around the typical red brick block appartements in Portland. Last two elements are typical and proper to NY.
Do you were in New York already ? There's not just Manhattan.
Those builduings strongly recall Portlands DT district
From Portland to Staunton
I have the feeling I'm standing in the red light district
"A comparison of the same present pre-release screenshot (as of April 2006) from GameSpot (top), among several gaming websites, and the official Grand Theft Auto III website (bottom). GameSpot's version depicts police cars resembling those of theNYPD pre-2000, while the official, edited version adopts a more generic black-and-white design used by many police departments such as the LAPDand SFPD."
Of course, nothing's 1:1, and the city is only loosely based on NY, also mixed with Chicago & Detroit. There's a lot of things missing, but overall Liberty City ressembles NY, without imitating it like in IV, where a lot of things are very accurate, or LS on LA or SF.
LC is definitely an North-east state like you said it, but the most influences come from NY.
EDIT : Be careful, one member said "it's not even close to NY", there is were I disagree, I never said it was a remake.