On long days, we just carried a regular backpack that had some snacks and water bottles, medicine I needed, other odds and ends. (We are strollerless.) We kept our wallets and DSLR in there as well. (I prefer to take my own pictures instead of Memory Maker.)
On days we didn't need as many provisions, and on one rainy day, I carried this purse which is a cross-body style that lays somewhat flat against your body.
I would just keep the bare minimum in it, and because it was so light and has such as a small footprint, I didn't have to take it off for any rides. We had pretty much all our souvenirs delivered to our room from the stores we brought them in unless they were small.