The 1950 CCNY Team, National Champions.
Note: That's calendar year, January 1 to December 31 -- not schoolyear, July 1 to June 30.
1950: City College of New York (CCNY) won the NCAA Tournament, and the New York Yankees won the World Series.
1963: Loyola University of Chicago won the NCAA Tournament, and the Chicago Bears won the NFL Championship.
1965: The University of California at Los Angeles (UCLA) won the NCAA Tournament, and the Los Angeles Dodgers won the World Series.
1972: UCLA won the NCAA Tournament, and the Los Angeles Lakers won the NBA Championship.
1989: Michigan won the NCAA Tournament, and the Detroit Pistons won the NBA Championship. The Crisler Center is 54 miles from the site of The Palace of Auburn Hills. This is close enough for me to count it as the same metropolitan area, but it's certainly not the same city.
2018: The Philadelphia Eagles won the Super Bowl, and Villanova University won the NCAA Tournament.
New York had a close call in 1952: The Yankees won the World Series, but St. John's University lost the NCAA Final.
In 1961, the University of Cincinnati won the NCAA Tournament, but the Cincinnati Reds lost the World Series.
In 1976, Indiana University won the NCAA Tournament, and the Cincinnati Reds won the World Series. However, despite the Reds being the closest MLB team to IU, the distance of 127 miles from Assembly Hall to Riverfront Stadium, and the crossing of a State Line, means this doesn't count.
In 1980, the Lakers won the NBA Championship, but UCLA lost the NCAA Final.
In 1996, the Yankees won the World Series, but Syracuse University lost the NCAA Final. Besides, the JMA Wireless Dome (then the Carrier Dome) is 252 miles from Yankee Stadium, so it wouldn't have counted, anyway. Nor would 2003, when Syracuse won the NCAA Final, but the Yankees lost the World Series, have counted.
In 2001, the Arizona Diamondbacks won the World Series, but the University of Arizona lost the NCAA Final. Besides, the McKale Center in Tucson is 114 miles from Chase Field (then Bank One Ballpark), so I probably wouldn't have counted it, anyway.
In 2004, the University of Connecticut won the NCAA Tournament. The New England Patriots won the Super Bowl, and the Boston Red Sox won the World Series. However, Gampel Pavilion Storrs, Connecticut is 74 miles from Gillette Stadium in Foxborough, Massachusetts; and 82 miles from Fenway Park in Boston. And, unlike Ann Arbor and Auburn Hills in Michigan, it's not in the same State. So I chose not to count it.
In 2005, the Chicago White Sox won the World Series, but the University of Illinois lost the NCAA Final. Besides, the State Farm Center (then Assembly Hall) in Champaign is 132 miles from Guaranteed Rate Field (then U.S. Cellular Field), so I probably wouldn't have counted it, anyway.
In 2006, the University of Florida won the NCAA Tournament, and the Miami Heat won the NBA Championship. However, Gainesville is 338 miles from Miami, so that can't be counted.
In 2019, the University of Virginia won the NCAA Tournament, and the closest MLB team, the Washington Nationals won the World Series. However, Charlottesville, Virginia is 119 miles from D.C., and a State Line must be crossed, so I can't count it.
The 2024 Final Four teams are, in alphabetical order: Alabama, Connecticut, North Carolina State and Purdue. The Kansas City Chiefs have won the Super Bowl, but can't be paired up with any of these schools. Alabama, in Tuscaloosa, is too far, even from Atlanta, to match up. Connecticut has already been ruled out.
North Carolina State is in Raleigh, so a Stanley Cup win by the Carolina Hurricanes, which is currently possible, would work; but the NBA's Charlotte Hornets are 162 miles away, so that pairing wouldn't work. And Purdue is in West Lafayette, Indiana: It's 69 miles from the Indianapolis teams, and nearly twice that from the Chicago teams, so it would be a judgment call if any of the applicable teams should be counted.