Has there ever been a U.S. city where their MLB, NFL, NHL, and NBA teams all won their respective championships in the same year?

(Within a 10 year span)

Although New York has the advantage of having multiple teams in all of these leagues, the city that comes the closest to accomplishing this feat is Boston: "When the Bruins reached the 2011 Stanley Cup Finals, the city of Boston became the first city in the 21st Century to have all four of its major professional league teams win a league championship, and it is the only city ever to have championships in all four major professional leagues within a ten-year span (from the Patriots' victory in February 2002 to the Bruins' in June 2011).[2] In just ten years, between February 2002 and June 2011, Boston's teams completed what Sports Illustrated dubbed as the "Grand Slam of North American sports"." -from https://en.wikipedia.org/wiki/Sports_in_Boston

(I acknowledge that the New England Patriots are no longer known as the Boston Patriots- they are still Boston's NFL team).

(Within One Year)

No U.S. (or Canadian) city has ever won all four major sports championships in the same year.

However, before the NBA was formed in 1946, one city DID win all three major sports (MLB, NFL, NHL) championships in the same year, which is an equivalent achievement.

That city was Detroit, Michigan, and the year was 1935.

the Tigers, Lions and Red Wings all won their first championships in the same season (1935-1936)!

http://bleacherreport.com/articles/622947-detroit-city-of-champions-how-the-greatest-season-ever-impacted-the-lions

Another impressive feat: 2002 Los Angeles metropolitan area's Lakers and Angels won the NBA and MLB championships along with two other local teams of smaller leagues (the Sparks of the WNBA and the Galaxy of the MLS).

And that's it. Several cities have won two championships in the same year, but no one else has ever won three, even though the number of major sports championships increased from three to four. Just shows what a great year Detroit had back then.

If you are interested in all of the two-win cities and other details, the following link is thorough:
https://en.wikipedia.org/wiki/Multiple_major_sports_championship_seasons