The problem with Kauffman stadium is that it’s sort of out in the middle of nowhere. So there’s not a ton of things to do or places to eat around there.
But there are a few BBQ places around. Gates BBQ is the most well known in KC and you can’t go wrong there.
Big T’s is also good. Very similar to Gates I’ve found though a bit fattier of meat.
Finally there’s LC’s which is a favorite of many but I’ve never been so I can’t speak to it.
All three are within a few miles of Kauffman.