There's a lot of data in the TBC data repository and here are some of the ways to mine the data at no cost. There's a mini-application for all levels of data from at bat level to career.
Play Index
At-bat level data for any Major League at bat since 1957. More than twenty different parameters to select from including batter/pitcher matchups.
Get at bat level splits for batters or pitchers for a combination of 2 dozen categories. Example: Between 1990 and 1999, which players had the most doubles at home in April while leading off.