Have each member of the family pick a favorite player and make T-shirts and signs rooting him on. Make signs for your home team too, and wave them high—if the game is being televised, that's your best bet for getting on camera!
Have a baseball movie marathon before you go. Little Big League, The Sandlot and Angels in the Outfield are all family-friendly baseball flicks. Then, let your kids feel like ballplayers themselves by getting tickets on the day of a Run the Bases promotion, when stadiums let kids on the field to run around the bases before the game.
Bring lunch, as ballpark food can get expensive, but give each member of the group a budget to buy one souvenir, like a foam finger, an ice cream sundae in a baseball helmet or a pack of baseball cards. Try to score tickets on a giveaway day, and you could come home with a free bobblehead, T-shirt or baseball cards.