The Braves play at Disney, and that would be the closest, although not the best in my opinion.
Lakeland is a great place to watch a game on the outfield grass, where there is plenty of room to not feel crowded.......bring a blanket if you do this.
After the game, head to the square in downtown Lakeland and visit Harrys Seafood and Steakhouse(modest prices)........tell them Fishhead sent ya.