The Rent book has photographs of a lot of the East Village locations that provided inspiration for the set design. You might want to check that out first.
The entire isle of Manhattan today looks nothing like it did in the 1990's! Maybe you should try parts of Brooklyn, although you will have a hard time trying to replicate the East Village of the 1990's.
I agree, the city has really built up in the past 20 + years, including the burnt out South Bronx. LES/East Village (as well as other areas) were slumming back then, alphabet city filled with starving artists, junkies, squatters and dilapidated buildings. There are probably no neighborhoods that resemble that right now. You can walk around St Marks, hang in Washington Square park to get an artsy feel, walk around Alphabet City and imagine what it looking like back then. But you will not get that slumming/bumming feel. May run into a few starving artist though, LOL!