Wow you and I sound so alike... I am always searching for fresh fruit at WDW especially when my kids were little. I felt like all they ate was burgers, fries, mac and cheese!
Now I haven't been in 4 years

but don't feel bad I'm going back in Feb.
So here are some places we got fruit last trip...
MK: Toon Town had a fruit stand, whole fruits, some cut up veggies. I remember buying bananas, baby carrots and oranges.
Studios: There was a fruit stand (Anaheim Produce?) right across from Beauty and Beast. You could get whole fruits or cut up fruit salads which were really good.
Epcot: Sunshine Seasons had some fruit, and there was a stand past Norway? African Outpost or something like that.
BW Bakery: we stayed in Epcot area and always bought bananas and fruit salads there.
Don't worry, you will find it. Just ask a CM if you can't find what you want.