I have a friend who has seen a home game of all 30 MLB teams, completing the trick in September 2013 when I joined him for a game in Toronto.
My friend is now backtracking to see the new stadiums of teams that have built since his last visit. He returned to Minnesota last year and this season visited Houston, Miami and Atlanta. If I'm not mistaken, the new Busch Stadium in St. Louis is the only current stadium he has not visited.
In 2010 we saw MLB games at six East Coast stadiums, starting with Fenway Park, in eight days (we also saw three plays and toured the Gettysburg Battlefield). The previous year we saw MLB games in four Southwest stadiums in only three days. After watching our Trail Blazers on a Friday night, we flew to Long Beach Saturday morning, saw the Red Sox play the Angels that afternoon and the Padres host the Giants that evening. After attending a 7 am Easter Mass, we flew to Phoenix to see the Diamondbacks host the Dodgers on Sunday afternoon before flying back to San Diego. The following day we were in attendance for the Dodgers' home opener against the Giants.
I still have not seen MLB games in Pittsburgh, Cincinnati, Detroit, Milwaukee, Atlanta, Miami, Tampa Bay and Houston. I have not seen the new stadiums in Minnesota (although I attended games at the two previous venues), St. Louis and Texas.