A cafeteria riddle is:
   
Q: Where do baby cows eat lunch?
A: At a calf-ateria.
 
The riddle has been cited in print since at least 1991.
 
         
Wikipedia: Cafeteria
A cafeteria, sometimes called a canteen outside the U.S., is a type of food service location in which there is little or no waiting staff table service, whether a restaurant or within an institution such as a large office building or school; a school dining location is also referred to as a dining hall or lunchroom (in American English). Cafeterias are different from coffeehouses, although the English term came from Latin American Spanish, where it had and still has the meaning “coffeehouse”.
     
Newspapers.com
29 January 1991, The Times Leader (Wilkes-Barre, PA), “Mighty Funny’s Mini Jokes,” pg. 4B, col. 1:
WHERE DO BABY COW GO TO EAT LUNCH?
IN THE CALF-ETERIA!
   
Google Books
Class Act:
Riddles for School
By John Jansen
Minneapolis, MN: Lerner Publications
1995
Pg. ?:
Q: Where do baby cows eat their school lunches?
A: In the calf-eteria.
 
Google Groups: alt.support.depression.recovery
Kids Jokes
.(JavaScript must be enabled to view this email address)
Feb 20, 1998, 3:00:00 AM
(...)
Where do baby cows eat lunch?
At a calf-ateria.
   
Google Groups: alt.teens
Lunch Time.
merrym8299
Feb 7, 2001, 5:11:31 PM
1. Where do baby cows have lunch? At the cafeteria.
       
Google Books
Ridiculous Riddles
By Chris Tait
New York, NY: Sterling Publishing Company, Inc.
2003
Pg. 85:
Where do baby cows go to eat lunch?
The calf-a-teria!
 
Twitter
Andrew Black
@andrewmblack
Where do baby cows eat? The calf-eteria.
6:59 PM · Jun 16, 2009·Twitter Web Client
 
Twitter
Hyperion
@HyperionEmpire
Q: Where do Baby Cows eat lunch?
A: The Calf-eteria
[*Popsicle-stick Joke]
12:26 AM · Jul 11, 2017·TweetDeck
 
Twitter
Eve Baskin
@ohyesitseve
“Where do baby cows eat lunch?
“The Calf-eteria”
@NeaNea005 this reminded me so much of you. Lollll
10:57 PM · Feb 9, 2020·Twitter for iPhone
 
Twitter
Jimmy RevJim Olsen
@mybuddyjimmy
Where do baby cows go to eat lunch? At the calf-eteria. #LaughoftheDay
3:49 PM · Apr 28, 2020 from Des Moines, IA·Twitter for iPhone