As the OP seems to be coming from Israel, buying stuff from home won't likely be an option
First, do your hotel rooms have fridges? That will be necessary for storage of milk, cheese, yogurt, etc.
(I live in a city in Canada where it's still hovering around the freezing mark at nights, so I was almost going to suggest you could keep those things in your rental vehicle if you didn't have a fridge... however, I see the weather in STL is MUCH nicer than what we've got here
)
My second question is one of timing... I see that events start as early as 7:30am on Saturday. I'm going to consider it a miracle if I manage to get any breakfast at all that day, let alone a nice picnic in a park...
How do you guys all do it?