Bananas keep fresh longer by hanging them up (as if they were still on the tree.) They sell little hangers in the kitchen section of Walmart and Bed, Bath, and Beyond or other kitchen stores for this. They are wooden and have a little hook to hang the bunch of bananas from.
Grapes can be washed and kept in a bowl in the refrigerator. They are also good treats when eaten frozen, but make sure you are slicing them in half for you daughter since they are a choking hazards.
For salads, we wash only what we need each time. I find that bagged salads go bad faster than if I buy a head of lettuce and keep it wrapped tightly and only slice off what we need at each meal. If you wash the whole bag or the whole head of lettuce and then refrigerate it for later, it will go bad faster.
My daughter loves fresh pears. They take a few days to get soft enough to eat, so maybe you could buy a few of these and let them ripen on your counter and let her eat the other things first, then you will have something to give her on the days when other things have been eaten already!
Apples keep for quite a long time too. You can leave them on the counter or put them in the refrigerator. If you peel and slice them ahead of time, you can put a little lemon juice in with the slices so they won't turn so brown, then store them in ziplock bags or covered bowls.
Also, any food stored with bananas will ripen more quickly because of the gas that bananas give off. You can ripen a fruit faster by putting it in a brown bag overnight with a banana!
Hope this helps!
-Amanda
