Manhattan-born actress Sylvia Miles got a reputation for appearing at many New York City openings and parties. American puppeteer Wayland Flowers joked about Miles, “She’d go to the opening of an envelope.”
 
“She’d go to the opening of an envelope” has been cited in print since June 1975. “Gadabout Sylvia Miles, has begun to like Wayland Flowers’ line, ‘She’ll go to the opening of an envelope’” was cited in October 1975.
 
Providence (RI) Mayor Buddy Cianci was known for attending many events in his city, and the “attend the opening of an envelope” line was applied to Cianci and other politicians.
 
     
Wiktionary: opening of an envelope
Noun
opening of an envelope
1. (idiomatic, humorous) Any kind of event or activity that may contribute to one’s self-promotion.
 
Wikipedia: Sylvia Miles
Sylvia Miles (born September 9, c. 1932) is an American film, stage and television actress, twice nominated for an Academy Award. She was born and raised in Greenwich Village, where her father was a furniture maker.
(...)
Wayland Flowers and his puppet Madame first uttered the widely quoted line “Sylvia Miles and Andy Warhol would attend the opening of a sewer”. Another source quotes Flowers as saying, “Sylvia Miles would attend the opening of an envelope”, while in 1976, People Magazine repeated the same joke without offering a source.
 
Wikipedia: Buddy Cianci
Vincent Albert “Buddy” Cianci, Jr. (/siˈænsi/, see-an-see; Italian pronunciation: [ˈtʃaŋtʃi], chahn-chee; born April 30, 1941) is an American politician who served as the mayor of Providence, Rhode Island from 1975 to 1984 and again from 1991 to 2002. Cianci is the longest-serving mayor of Providence, and one of the longest-serving “big city” mayors in United States history, having held office for over 21 years.
 
Notably, he was forced to resign from office twice due to felony convictions. His first administration ended in 1984 when he pleaded guilty to assault. His second stint as mayor ended when he was forced to resign following his conviction for racketeering conspiracy (running a corrupt criminal enterprise), and he served four years in federal prison.
(...)
Cianci was well known as an extremely charismatic and media-savvy politician. His propensity to attend parades, weddings, public events, and backyard neighborhood barbecues led to a common joke during his tenure that Cianci would jump to attend the opening of an envelope.
 
Google News Archive
19 June 1975, Pittsburgh (PA) Post-Gazette, “It Happened Last Night” by Earl Wilson, pg. 12, cols. 3-4:
Ventriloquist Wayland Flowers saw Fanne Foxe in his audience at Grand Finale and said, “I understand you’ve been through the mills.” of gadabout Sylvia Miles: “She’d go to the opening of an envelope.”
 
Google News Archive
14 July 1975, Milwaukee (WI) Sentinel, Earl Wilson syndicated entertainment column, pt. 1, pg. 15, col. 1:
The busiest gadabout gal was actress Sylvia Miles. Ventriloquist Wayland Flowers said, “She’d go to the opening of an envelope.”
 
Google News Archive
9 October 1975, Beaver County (PA) Times, Earl Wilson syndicated entertainment column, pg. B-8, col. 1:
Gadabout Sylvia Miles, has begun to like Wayland Flowers’ line, “She’ll go to the opening of an envelope.”
 
People magazine
October 18, 1976 Vol. 6 No. 16
What Would a Manhattan Party Be Without the Ubiquitous Sylvia Miles?
By Judy Kessler
She shows up at premieres, screenings, receptions, teas and charity cocktail parties. The joke is that Sylvia Miles would attend the opening of an envelope.
 
Google News Archive
11 April 1977, The Blade (Toledo, OH), Earl Wilson syndicated entertainment column, pg. P-3, col. 1:
She had once said that puppeteer Wayland Flowers’ puppet, “Madam,” wasn’t very feminine. Madam retorted, “That’s Sylvia Miles! She’d go to the opening of an envelope!”
   
Google News Archive
5 June 1984, Rome (GA) News-Tribune, “Night of the full moon” by James Brady, pg. 4, col. 3:
There are New Yorkers who will attend the opening of an envelope.
 
Google Books
But Enough About You
By Cynthia Heimel
New York, NY: Simon & Schuster
1988
Pg. 122:
People have said that Sylvia would attend the opening of an envelope. This is not true. There are no VIP areas or free drink tickets involved in envelope openings.
     
Google Books
The Prince of Providence:
The Rise and Fall of Buddy Cianci,  America’s Most Notorious Mayor, Some Wiseguys and the Feds
By Mike Stanton
New York, NY: Random House
2004, ©2003
Pg. XII:
Cianci was a spellbinding speaker and ubiquitous politician who. in a line borrowed from Andy Warhol. joked that he would attend the opening of an envelope.
 
Google Books
The Mammoth Book of Insults
By Geoff Tibballs
London: Constable & Robinson Ltd.
2007
Pg. ?:
She was so hungry for publicity that she would attend the opening of an envelope.
 
The Weekly Standard
The Buddy System
Providence has changed. Has he?
SEP 29, 2014, VOL. 20, NO. 03 • BY ETHAN EPSTEIN
Providence
Buddy Cianci does not have a cold.
(...)
As the old joke goes, Cianci is the kind of politician who would have attended the opening of an envelope.