Yes, there's a bunch of fruit stands. Seems like many of the counter service places also have fresh fruit available. Also, in California adventure, we had good fruit at a stand in Hollywood backlot, and Bakersfield bakery had some fruit, too, as well as yogurt parfaits.
We liked Whitewater Snacks in the GCH. They had fresh, cut-up fruit or veggie trays that you could grab and go. I could grab one of each and it was plenty for my 3 big girls to share.
The other thing was that we ordered groceries from Albertsons and had them delivered to the hotel. You can order 3 bananas, 4 apples, 1 lb of grapes, whatever you want. We found it very convenient to have breakfast foods in our room, as well as a rack of bottled water.