Woolacombe, Devon, UK, appears to be the closest. I think it’s safe to say it’s over 500 miles.
Thank goodness for those who have never visited the USA not taking sides against New Orleans and showing the same love for NYC. There are still quite a few who voted in the New Orleans poll who have yet to give NYC the same treatment.
I’ve never lived in New York City but I’ve lived nearby and have visited the citizen on numerous occasions.
Been twice: once in 1967 and once at Christmas in 2002.
Lived in Brooklyn and worked in Manhattan for three years.
Lived in Manhattan for a total of 5 years (three as a child, two as an adult).
Well, I haven’t been to either, but this poll caught my eye. I just didn’t see the New Orleans poll, to be quite honest.
Here’s a comparison between the New Orleans poll and the New York City poll at 132 Voters. The link in the OP has the New Orleans numbers.
Meanwhile the New Orleans poll has moved on and it will be fun to see how the New York City numbers change as they reach bigger numbers of Voters.
Geography Trivia: What's the closest (in miles)
that you have ever been to New Orleans?
Right there! 97 73.48%
1-20 miles 1 0.76%
21-50 miles 2 1.52%
51-100 miles 2 1.52%
101-500 miles 20 15.15%
over 500 miles 10 7.58%
Voters: 132
View Poll Results: What's the closest (in miles)
that you have ever been to New Orleans?
Right there! 136 71.58%
1-20 miles 2 1.05%
21-50 miles 2 1.05%
51-100 miles 2 1.05%
101-500 miles 32 16.84%
over 500 miles 16 8.42%
Voters: 190
View Poll Results: What's the closest (in miles)
that you have ever been to New York City?
Been right there! 118 89.39%
1-20 miles 2 1.52%
21-50 miles 1 0.76%
51-100 miles 0 0%
101-500 miles 3 2.27%
over 500 miles 7 5.30%
New Jersey 0 0%
Connecticut 0 0%
Upstate New York 1 0.76%
Pennsylvania 0 0%
Massachusetts 0 0%
Voters: 132
First impression would suggest that New York City is indeed more likely to have had more Dopers there than New Orleans.
Who wants to test out Chicago, Las Vegas, or some other city?
You need an option for “Thousands of miles”. 
I thought that “over 500 miles” would cover the “ain’t never been close” group.
Been there two or three times. Had a close friend who lived near Times Square.
Haven’t been back in a few years, though. I should find an excuse.
-D/a
I was there until the CHUDs came out.
3200 miles (Aberdeenshire, Scotland in 2002).
Visited the city in 2009. Hope to go back some day – didn’t have nearly enough time to explore.
I lived in, or around, NYC for 25 years. Wish I were still there.
In hindsight, I realize this was a pretty poor answer to your query so to make amends we have planned to visit there in the fall. I will hit the museums and the missus will do her best to pump some dollars into the local economy.
I just hope you were planning that before this thread! I’d hate to have that experience blamed on me. 
Seriously, though, there have been other threads and discussions where the issue has been “what does it take for you to say you’ve “been to” a place?”
Be a good poll …
So do it! I’ll play.
Washington, DC in junior high school. It’s the only time in my life I’ve been east of the Mississippi.