Depending on how much you would like to have with you, you may want to place an order with garden grocer (for convenience of having it available in the room). Then you could bring with you a small softsided cooler (or lunchbox thing) and pack an ice pack in your checked luggage (if the fridges have a freezer section? Otherwise bring ziploc bags and fill with ice to keep things cold.
Then you could order things like sliced apples (we just got them in our last order - nice to have), yogurts, fruit cups, juices, whatever your little one likes, maybe cheese slices, crackers,... Then pack a nice selection to go with you daily.
I used to bring a little cooler with juice, water, and some healthy snacks to the parks when my kids were little. I never knew when they'd need a little snack, and my DS has food allergies so I knew what was safe. I actually shipped a box down ahead of time a couple of times with safe snacks for him as well as a hot pot to heat water in the room for ramen (something my kids liked a lot and was safe to eat).
Like others have said, they do have a snack pack thing at some counter service places. You'll spend more that way though. I'd rather tailor it to what your little one likes.