Before moving to the area, I definitely did several trips to the world on the cheap. Recently, on a trip to CA we were gifted with a stash of bagels from a local artisan place and didn't have a fridge. I can offer the following suggestions.
1) Definitely eat breakfast in the room. I've done cereal and UHT/Parmalat milk and sometimes granola bars.
2) If you want to do something like bagels and cream cheese, I have discovered that putting cream cheese in your ice bucket and then putting ice on top of it, definitely functions as a fridge replacement. We replaced the ice in the morning and in the evening and it stayed cold and fresh with no problem.
3) If you're really into saving money, you can bring items that don't need refrigerating with you into the park to make sandwiches. We did those premade tuna cans when we went to Muir Woods in CA. You could even bring tuna pouches and get mayo at quick serve places. You could also bring Jif on the Go's, which are single serve peanut butters. You can get those at the Dollar Tree or even CVS.
4) If you're a little less frugal, I suggest eating at CS place like Pecos Bill. They have an awesome toppings bar that can really help bulk up your meal. I usually add a scoop of mushroom and onion to my burgers there. They also offer lettuce, tomatoes and dressing, so you could potentially even make a mini salad.
5) I find the kid's meal quality to be pretty comparable to adult meal quality - it's just the portion sizes that are different. If you're not big eaters, I definitely suggest getting the kids meals. They're a nice lunch time option.
6) Definitely bring portable snacks into the park with you! Maybe DD can choose something she likes on a supermarket trip?
All of that said, don't forget to have fun! If you go super frugal style, think about building in a few treats here and there - maybe afternoon ice cream or whatnot. Totally a treat in the hot FL sun!
