I've yet to have them tell me I couldn't bring something in, FWIW. I'm sure if I showed up carrying a pizza box, they might turn me away, but if you have a sack lunch in your backpack, they probably won't stop you.
Here's what I usually take. I don't buy kids meals, so I try to have a drink on hand for DD3 so she can just share with us.
Milk boxes
Juice boxes
String cheese
Crackers
Fruit snacks
Trail mix
Fruit leather
Apple sauce pouches
Grapes/berries
Camelback full of water
I've never tried anything like a bottle of Coke or a sandwich, but I'm guessing they would let those in if you have them in a bag. Good luck! I'm sure it will be great!