“Why do we drive on the parkway and park on the driveway?”

“Why do we drive on the parkway and park on the driveway?” is a jocular question that has been cited in print since at least 1974, when this was printed in the Washington (DC) Post on March 17, 1974:
   
DEAR DR. BICYCLE: Since you drive on a parkway and park on a driveway, where do you bike?—J. K., Suffern, N.Y.
DEAR J.K.: In the street.
   
“John Sonderberg of Doylestown notes that we park on a driveway and drive on a parkway” was printed in the Philadelphia (PA) Inquirer on June 15, 1980. “A ‘howcum’ from Alan Wiemann: ‘Howcum we park in a driveway and drive on a parkway, not that I rully care?’” was printed in Herb Caen’s column in the San Francisco (CA) Chronicle on May 26, 1981.
   
The comedian Gallagher was credited for using the joke in his act (“Why do you park in the driveway and drive on the parkway?”) in the St. Louis (MO) Post-Dispatch on November 5, 1984. Gallagher probably helped to popularize the line.
   
       
17 March 1974, Washington (DC) Post, “Ask Dr. Bicycle,” pg. D16, col. 5:
DEAR DR. BICYCLE: Since you drive on a parkway and park on a driveway, where do you bike?—J. K., Suffern, N.Y.
DEAR J.K.: In the street.
   
15 June 1980, Philadelphia (PA) Inquirer, “Words &c” by John F. Gummere, pg. 18-L, col. 2:
John Sonderberg of Doylestown notes that we park on a driveway and drive on a parkway.
   
26 May 1981, San Francisco (CA) Chronicle, “Just Kiddin’ Around” by Herb Caen, pg. 27, col. 1:
A “howcum” from Alan Wiemann: “Howcum we park in a driveway and drive on a parkway, not that I rully care?”
 
21 March 1984, The Beacon Journal (Akron, OH), pg. 1, col. 2:
CHUCKLE: How come people drive on parkways and park in driveways?
   
13 August 1984, Daily Sitka Sentinel (Sitka, AK), “Burnt Toast” by L. M. Boyd, pg. 2, col. 4:
Sorry, our Language man cannot explain how it came to be that the idiom has us park in the driveway and drive in the parkway.
 
5 November 1984, St. Louis (MO) Post-Dispatch, “Gallagher Is At His Funniest—Most Of The Time” by Dick Richmond, pg. 4B, col. 4:
“Why do you park in the driveway and drive on the parkway?”
 
14 December 1985, Newsday (Long Island, NY), “Gallagher showers his fans with laughs” by Carl Pisano, pt. 2, pg. 25, col. 2:
He (Gallagher—ed.) think it’s stupid, for example, that we drive on the parkway and park on the driveway.
 
Google Books
More of the Straight Dope
By Cecil Adams (Ed Zotti)
New York, NY: Ballantine Books
1988
Pg. 80:
Why do we drive on the parkway and park in the driveway?— Deidra N., Baltimore
 
23 May 1989, The Plain Dealer (Cleveland, OH), pg. 6C, col. 6:
Houston Astros pitcher Larry Andersen is, well, kind of a strange guy.
(...)
For instance, he would like to know why you drive on a parkway and park on a driveway?
 
24 October 1989, Cedar Rapids (IA) Gazette, “Gallagher hammers home his message” by Dee Ann Rexroat, pg. 8A, col. 2:
You drive on a parkway, and park on a driveway.
 
Google News Archive
1 December 1989, Pittsburgh (PA) Press, “After the 2nd millennium a decade comes to naught” by Brian O’Neill, pg. B1, cols. 1-2:
I hadn’t been this perplexed since 1 heard a comic ask, “Why do people park on a driveway and drive on a parkway?”
 
Google Books
The Gospel Through the Windshield:
A Devotional for Drivers
By Joseph William Seaborn
Indianapolis, IN: Wesley Press
1990
Pg. 92:
It’s a little confusing, but in America we park on driveways and drive on parkways.
   
28 July 1991, Pittsburgh (PA) Post-Gazette, “Here’s the Pitch,” pg. D2:
The world’s 10 most perplexing questions, courtesy of San Diego Padres reliever Larry Andersen (drum roll, please):
(...)
Why do you drive on the parkway and park on the driveway?
 
Google Books
Naked Pictures of Famous People
By Jon Stewart
New York, NY: Perennial
2001, ©1998
Pg. 70:
Once, right before dessert, Jesus said to no one in particular, “Why do people park on a driveway and drive on a parkway?” It was kind of funny.