The best way to handle the "stuff in the stroller" dilemma is to try NOT to use the basket of the stroller for storage. I know, I know, that seems weird, but it's true.
Just think how much easier it is to transport a stroller if you don't have to stop to remove the contents of the basket every time you fold it. I learned long ago that the basket is a black hole that will slow you down if you let it. Instead of using it, I carry a lightweight cloth drawstring backpack that I sling over the stroller handles. Everything is stored there. When we park the stroller, we snatch the backpack off and take it onto the ride or into the restaurant. No fuss or bother, just grab and go, and all of our stuff is accounted for. (When DS was little and I had to carry food, we left a lunchpack cooler in the basket, but that was ALL that was in it.)
Of course, something that goes along with this strategy is the idea that you don't need to carry a lot of stuff into the parks with you. If it all needs to go into one backpack, you'll force yourself to pare down, and you will be very glad you did. Other than baby food/changing supplies, which we don't carry any longer, here is our list: digital camera, sunblock spray, sunblock stick, a small bottle of bubbles, park map, two flat cloth diapers in a large ziploc, a Brita filter bottle, an extra plain water bottle, rain ponchos, a ziploc of pretzels, and a change of clothes for DS. Park tickets are on lanyards around our necks, and my ID and money are in a string wallet around my waist. We all wear sport sandals, so no need for extra shoes. In parks where there are water rides, we also carry a plastic bag big enough to hold the entire backpack.
Key point: if you buy any souvies inside parks, DON'T leave the store with them!!!! Send them to your resort if you can, or have them held at the park entrance for when you leave. It's the best way to ensure that they do not get lost or broken.
