Believe me, I shared your incredulity. Leveraging the amazing power of Wikipedia, I constructed the following list of NL teams, their current park and year built, and their immediate former parks and years of use:
Atlanta Braves: Turner Field, 1997; Atlanta-Fulton County Stadium, 1966-1996
Florida Marlins: Dolphin Stadium, nee Pro Player Stadium, nee Pro Player Park, nee Joe Robbie Stadium, 1993 (will move to new stadium in 2011)
New York Mets: Shea Stadium, 1964 (will move to Citi Field in 2009)
**Philadelphia Phillies: ** Citizens Bank Park, 2004; Veterans Stadium, 1971-2003
Washington Nationals: Nationals Park, 2008; RFK Stadium, 2005-2007
Chicago Cubs: Wrigley Field, 1916
Cincinnati Reds: Great American Ballpark, 2003; Riverfront Stadium, 1970-2002
Houston Astros: Minute Maid Park, 2000 (nee Astros Field, Enron Field); Astrodome, 1965-1999
Milwaukee Brewers: Miller Park, 2001; County Stadium, 1970-2000
Pittsburgh Pirates: PNC Park, 2001; Three Rivers Stadium, 1970-2000
St. Louis Cardinals: Busch Stadium III, 2006; Busch Stadium II, 1966-2005
Arizona Diamondbacks: Chase Field, 1998 (nee Bank One Ballpark)
Colorado Rockies: Coors Field, 1995
Los Angeles Dodgers: Dodger Stadium, 1962
**San Diego Padres: ** PETCO Park, 2004; Qualcomm Stadium, nee Jack Murphy Stadium, nee San Diego Stadium, 1969-2003
San Francisco Giants: AT&T Park, 2000 (nee SBC Park, nee Pacific Bell Park); Candlestick Park, nee 3Com Park at Candlestick Point, 1960-1999
Wrigley’s an outlier; without the Friendly Confines in the mix, the average NL ballpark was built in (late) 1995; that’s including Dodger Stadium and not taking into account the opening dates for the Mets’ and Marlins’ new stadiums.