Using distance to from.net
www.distancefromto.net/here is a look at how far the facilities of the 3 major sports that play more than once a week are located from downtown. These may be off a few miles one way or the other because I'm not sure if this site uses the downtown exactly or the city center. For example on the site it says it's 17.4 from downtown Phoenix to Gila River arena, wiki says it's 12.5. Take these with a bit of a grain of salt this is not perfect by any means.
NHL
Team-Arena-miles
St. Louis Blues Scottrade Center(1994) 0.23
Nashville Predators Bridgestone Arena(1996)* 0.39
Edmonton Oilers Rogers Place(2016) 0.4
San Jose Sharks SAP Center at San Jose(1993) 0.67
Pittsburgh Penguins Consol Energy Center(2010) 0.7
Toronto Maple Leafs Air Canada Centre(1999) 0.71
Boston Bruins TD Garden(1995) 0.77
Montreal Canadiens Bell Centre(1996)* 0.8
Tampa Bay Lightning Amalie Arena(1996) 0.87
Columbus Blue Jackets Nationwide Arena(2000) 0.93
Buffalo Sabres First Niagara Center(1996) 1
Winnipeg Jets MTS Centre(2004)* 1.01
Detroit Red Wings New Detroit Arena(2017) 1.03
Vancouver Canucks Rogers Arena(1995) 1.17
Dallas Stars American Airlines Center(2001) 1.21
Washington Capitals Verizon Center(1997)* 1.32
Calgary Flames Scotiabank Saddledome(1983) 1.51
Los Angeles Kings Staples Center(1999) 1.88
Colorado Avalanche Pepsi Center(1999) 2.08
Minnesota Wild Xcel Energy Center(2000) 2.75 from downtown st. paul, 9.26 to minneapolis
Chicago Blackhawks United Center(1994) 3.07
New York Rangers Madison Square Garden(1968) 3.08
New York Islanders Barclays Center(2012) 3.25
Anaheim Ducks Honda Center(1993) 4.74 (from Anaheim not LA)
Philadelphia Flyers Wells Fargo Center(1996) 6.14
Carolina Hurricanes PNC Arena(1999) 6.53
New Jersey Devils Prudential Center(2007) 10.24 (there are great public transport options for this so the distance is misleading)
Tukwila 11.94
Ottawa Senators Canadian Tire Centre(1996)* 15.81 (want new arena downtown)
Arizona Coyotes Gila River Arena(2003)* 17.4(If i'm wrong and they lose the lawsuit or the city doesn't cave they are finished)
Florida Panthers BB&T Center(1998) 36.17 (want a bailout, if they ever separate the concerts from hockey good bye panthers)
NBA
Phoenix Suns Talking Stick Resort Arena(1992) 0.24
Oklahoma City Thunder Chesapeake Energy Arena(2002) 0.33
Indiana Pacers Bankers Life Fieldhouse(1999) 0.36
Sacramento Kings Golden 1 Center(2016) 0.49
Charlotte Hornets Time Warner Cable Arena(2005) 0.6
Cleveland Cavaliers Quicken Loans Arena(1994) 0.62
Orlando Magic Amway Center(2010) 0.67
Toronto Raptors Air Canada Centre(1999)* 0.71
Boston Celtics TD Garden(1995) 0.77
Memphis Grizzlies FedExForum(2004) 0.92
Milwaukee Bucks BMO Harris Bradley Center(1988) 1.06 (new arena will be in the same area)
Dallas Mavericks American Airlines Center(2001) 1.21
Portland Trail Blazers Moda Center(1995) 1.23
Houston Rockets Toyota Center(2003) 1.25
Utah Jazz EnergySolutions Arena(1991) 1.26
Atlanta Hawks Philips Arena(1999) 1.28
Washington Wizards Verizon Center(1997)* 1.32
Minnesota Timberwolves The Target Center(1990) 1.37
New Orleans Pelicans Smoothie King Center(1999) 1.5
Miami Heat American Airlines Arena(1999)* 1.54
Los Angeles Lakers/ Staples Center(1999) 1.88
Los Angeles Clippers 1.88
Denver Nuggets Pepsi Center(1999) 2.08
Chicago Bulls United Center(1994) 3.07
New York Knicks Madison Square Garden(1968) 3.08
Brooklyn Nets Barclays Center(2012) 3.25
San Antonio Spurs AT&T Center(2002) 4.01
Philadelphia 76ers Wells Fargo Center(1996) 6.14
Golden State Warriors Oracle Arena(1966)6.37 from Oakland, 17.35 miles to San Francisco (If they can beat back NIMBYS and get their privately financed arena in San Francisco they will be 2.78 miles from downtown)
Tukwila 11.94
Detroit Pistons The Palace of Auburn Hills(1988) 32.55 (owner is talking to the Illitches about move downtown)
MLB
Arizona Diamondbacks Chase Field(1998) 0.52
St. Louis Cardinals Busch Stadium(2006) 0.56
Cincinnati Reds Great American Ballpark(2003) 0.64
Minnesota Twins Target Field(2010) 0.7
Detroit Tigers Comerica Park(2000) 0.76
Baltimore Orioles Camden Yards(1992) 0.84
Pittsburgh Pirates PNC Park(2001) 0.9
San Diego Padres Petco Park(2004) 0.9
Cleveland Indians Progressive Field(1994) 0.93
Houston Astros Minute Maid Park(2000) 1.12
Seattle Mariners Safeco Field(1999)* 1.2
Toronto Blue Jays Rogers Centre(1989)* 1.52
Los Angeles Dodgers Dodger Stadium(1962) 1.86
Colorado Rockies Coors Field(1995) 2.05
San Francisco Giants AT&T Park(2000) 2.21
Boston Red Sox Fenway Park(1912) 2.47
Miami Marlins Marlins Park(2012) 3.09
Washington Nationals Nationals Park(2008) 3.52
Los Angeles Angels Angels Stadium(1966) 4.02
Milwaukee Brewers Miller Park(2001) 4.16
Chicago White Sox US Cellular Field(1991) 4.72
Oakland A's O.co Coliseum(1966)* 6.66
Chicago Cubs Wrigley Field(1914)* 6.82
Philadelphia Phillies Citizens Bank Park(2004) 6.82
Kansas City Royals Kauffman Stadium(1973) 7.59
New York Yankees Yankee Stadium(2009) 11.65
New York Mets Citi Field(2009) 13.24
Atlanta Braves SunTrust Park(2017) 13.82 (all the white fans live in the North suburbs so this may work)
Texas Rangers Globe Life Park in Arlington(1994) 17.91 from dallas 15.4 miles from Fort Worth
Tampa Bay Rays Tropicana Field(1990) Renovated (1998)* 22.58 (want replacement because of location)
New York is so built up that the miles on this one are misleading. There's plenty of people in the Bronx, Queens and there are great public transport options for both stadiums.
Here is the NFL for the heck of it
Cleveland Browns FirstEnergy Stadium(1999) 0.55
Detroit Lions Ford Field(2002) 0.67
Carolina Panthers Bank of America Stadium(1996) 0.75
Minnesota Vikings U.S. Bank Stadium(2016) 0.75
Indianapolis Colts Lucas Oil Stadium(2008) 0.81
Cincinnati Bengals Paul Brown Stadium(2000) 0.85
New Orleans Saints Mercedes-Benz Superdome(1975) 0.86
Tennessee Titans Nissan Stadium(1999) 0.88
Atlanta Falcons New Atlanta Falcons Stadium(2017) 1.04
Seattle Seahawks CenturyLink Field(2002) 1.07
St. Louis Rams Edward Jones Dome(1995)* 1.17
Jacksonville Jaguars EverBank Field(1946) 1.29
Pittsburgh Steelers Heinz Field(2001) 1.33
Baltimore Ravens M&T Bank Stadium(1998) 1.47
Chicago Bears Soldier Field(1924) 2.21
Denver Broncos Sports Authority Field at Mile High(2001) 2.66
Green Bay Packers Lambeau Field(1957) 3.12
Tampa Bay Buccaneers Raymond James Stadium(1998) 4.72
Philadelphia Eagles Lincoln Financial Field(2003) 6.4
Oakland Raiders O.co Coliseum(1966) 6.66 from Oakland
San Diego Chargers Qualcomm Stadium(1967) 7.18
Kansas City Chiefs Arrowhead Stadium(1972) 7.9
Houston Texans NRG Stadium(2002) 8.91
New York Giants/ MetLife Stadium(2010) 11.16
New York Jets 11.16
Buffalo Bills Ralph Wilson Stadium(1973) 11.5
Washington Redskins FedEx Field(1997) 11.61
Miami Dolphins Sun Life Stadium(1987) 16.05
Arizona Cardinals University of Phoenix Stadium(2006) 16.62
Dallas Cowboys AT&T Stadium(2009) 18.21
New England Patriots Gillette Stadium(2002) 27.25
San Francisco 49ers Levi's Stadium(2014) 42.14 from San Francisco, 8.53 miles to San Jose