It is often hard to find at WDW. This is a big reason why we often do a grocery store run ourselves.
Some WDW places I have had luck: WDW now stocks Cuties tangerines in a fair number of locations: the in-park fruit stands, as a side with some QS meals. Another place we find fruit is the breakfast buffet when we stay club level.
Sad to say, but this is one reason why we sometimes choose club level. By that I mean every food court ought to offer it, but since it is hard to find, part of why we choose to stay club level is that we can readily get fresh produce every day. In the morning the lounges have fresh fruit, and during appetizers many CL's put out cold vegetables like grape tomatoes, broccoli, small carrots (sometimes the gross WDW packaged ones now, but often better quality carrots too), sometimes cucumber sticks, etc. I've even sometimes seen asparagus! The CL's also usually put out a basket of whole fruit all day, that is just okay. It varies from stay to stay. Recently they have had Cuties, but often it is just bleh apples, maybe underripe pears, Sunkist meh oranges. During breakfast hours (7am-10am), the CL's have better fruit. It varies from CL to CL and visit to visit, but they often have melon, good red grapes, sometimes: pineapple, strawberries, other berries.
Other places to find fruit: the QS in the Land (Epcot) usually has something like grapes or a melon cup. (not the gross baggies, but a better cup of grapes). Some table service buffets. One place that has a great salad is Docking Bay 7! it has grapes, tomato, cucumber, and really great dressing. The kefta appetizer is also really good. The grab and go places at the Swan/Dolphin/Swan Reserve.
It is possible to find some decent produce at Universal. Some that come to mind: The Harry Potter Hogsmeade has a fruit cart. Leaky Cauldron has bangers and mash - sausage- but it some with excellent sides. The minted peas are delicious. You have to ask, but they allow you to order the peas stand alone. the whole platter is very good though. The apple beet salad is also good (comes with a different platter). Portofino QS Sal's has prepared salads including caprese, some fruit. The club level lounges at Royal Pacific and Portofino Universal both serve great fruit in the AM and decent veggies during appetizer hours. thunder Falls Terrace is decent. the roasted corn on cob is not great, but the other sides are good, like plantains. Aventura food court has some good options, as does the Qs at Sapphire Falls. The QS at SF has fruit smoothies (or did the last time I was there.) Morning grab and go in the lobby at Royal Pacific, but I don't recall what they had- only available in the morning.
In season, there are some offsite places to get fresh oranges. there's a fun (but so-so) fruit stand on Route 192, and (I've not been) a better orange grove/fruit place I think about 20min from WDW. If you ever drive to the Everglades, you can get AMAZING exotic tropical fruit at a fruit stand called Robert is Here, and other smaller fruit stands. RiH will cut up the fruit for you, including amazing mangoes. They also make smoothies with I think any fruit they sell. You can try some really exotic fruits there like soursop.
Just off Universal is a Whole Foods. It is an excellent Whole Foods with a LARGE buffet of prepared foods, or did last time I was there. It is on Sand Lake Road. They recently remodeled, so I can't say exactly what they offer now, but I am sure they still have a very large offering of all kinds of healthy options of prepared foods, plus like a full bakery, etc. pricey, but a large selection for fresh produce. There are plenty of other good grocery stores, too, but that WF was a cut above, if a bit $$.