While 78 percent of Democrats and 60 percent of independents want the convention, 52 percent of Republicans hope the Democrats go some place else, the Quinnipiac University poll said.
Two-thirds, 67 percent, of respondents agreed that Brooklyn is the current "hip place" in the city. By a 47-39 edge, they picked Brooklyn over Manhattan as the convention site.
Support for Brooklyn was strongest in Brooklyn (54 percent to 34 percent) and Manhattan (53-31). Queens voters were almost evenly split at 42-40, while 55 percent of voters in Staten Island and half in the Bronx gave Manhattan the edge.
"Haven't you heard? Brooklyn is now hip! The city's pitch is to stage the show in Brooklyn -- and Brooklyn likes that a lot," Maurice Carroll, the poll's assistant director, said. "Manhattanites think the convention ought to be in Brooklyn, too. Are they being gracious, or ducking the traffic?"
The Democrats held their 1976 and 1980 conventions in Madison Square Garden in New York City, nominating Jimmy Carter at both. The Republicans held their 2004 convention in the same place, nominating George W. Bush for a second term.
The Republicans have settled on un-hip Cleveland for 2016.
Quinnipiac polled 1,021 New York voters between Aug. 20 and Aug. 25. The margin of error for the entire sample is 3.1 percentage points.