Babe Ruth, perhaps baseball's greatest ever player, was born on this day in 1895 in Baltimore, Maryland. He defined the early greatness of the Yankees and established it as baseball's greatest club. His transfer from the Boston Red Sox also helped define one of baseball's greatest rivalries.
The most relevant place to experience Babe Ruth in New York of course is Yankee Stadium, even though it's not the Yankee Stadium that Babe Ruth played at. The original was torn down into in 2008. The new Yankee Stadium contains the Yankee Stadium museum which contains player memorabilia and Monument Park, and open air museum featuring retired numbers as well as plaques honoring famous Yankees. Unfortunately Monument Park is closed in February but access it is included in tickets to Yankee games.
You can also visit the Ansonia apartment building, where he lived for a time, at 72nd and Broadway. You can have an ale at McSoreley's on 7th Street, a bar he drank at. You can also visit his grave at the Gate of Heaven Cemetery in Westchester County north of the city. It can be accessed by train from Grand Central; the stop is Mount Pleasant. A number of other baseball players are buried there.