Well, it's no Yankee Stadium—hell, it's no Shea Stadium—but Moscow does have its very own ballpark, on a scenic plot on the campus of Moscow State University (the frilly tall building down the leftfield line). The press box is nice, it's got a bar (this is Russia), a clubhouse shop, and some extremely ratty astroturf (god help anyone who slides). The scoreboard, alas, has never worked. The place was built in 1989, with money from a Japanese businessman.
If you're in town this weekend, be sure to drop in for the Russian World Series: a round-robin tournament with the teams from Moscow's A League.