Usually baseball stadiums allow you to bring in sealed beverages. They have to be sealed though and they will check from my experience.
Food is usually OK as well as long as it is clearly visible what the item is (like, in a clear ziplock and not a brown bag).
From the Cardinal website:
"In conjunction with a league-wide policy established by Major League Baseball, the St. Louis Cardinals reserve the right to inspect all items entering Busch Stadium. Guests may carry in items including: backpacks, purses, diaper bags, fanny packs and soft-sided coolers that do not exceed a maximum size of 16"x 16" x 8". Bags that exceed this size are not permitted in the stadium. Alcohol, bottles, cans, thermoses, hard-sided coolers, hard plastic cups/mugs are not permitted. Non-alcoholic beverages including water and soda in open cups or in clear plastic bottles no larger than 2 liters are allowed. All items will be inspected. Those patrons who refuse a search will be denied entrance into the stadium. Exceptions may be made for medical considerations."
More information can be found here: http://stlouis.cardinals.mlb.com/stl/ballpark/ballpark_guide.jsp