It's been years since I was there, but the sort of food court that's out beyond centerfield used to be filled with local (non-Aramark) options.
They also used to be more liberal than most parks in letting you bring in outside food/drink, though I don't know what the rules are now. One of my friends would always stop at Tony Luke's for a cheesesteak on the way to the park; another (more thrifty) friend would stop at a nearby gas station and pick up a water or soda to take in.