My son (was 7 on last visit to WDW) is not a 'picky eater' at all, and enjoyed the food everywhere we ate within WDW... including the ethnic foods in the different countries at WS.
But these are his favorites:
1. MK -- Crystal Palace for sit down/Character meal, and Casey's Hot Dogs for counter service.
2. Epcot -- Garden Grill for sit down/Character meal (loves the Ice Cream Social at GG), and most any counter service options in WS, but particularly China ('Lotus Blossom', where he highly recommends the Ginger ice-cream!) Looking forward to grazing our way through the F & W Festival this October.
3. MGM/DS -- Sci Fi for sit down, and Pizza Planet for counter service. ('Themeing' tends to win out over food quality when in this park.)
4. DAK -- Rain Forest Cafe for sit down meal, and the Chakranadi Chicken Shop for counter service (DS loves Asian food).
5. Non-Park -- We really don't eat much outside of the parks, since we can always 'hop' to Epcot for a quick bite... but DS(now 9) is especially looking forward to trying out Avalunch at Blizzard Beach this time around.
Tip #1 - You can view menus for any of the WDW restaurants online, prior to your trip. Doing so should give you a fairly good idea of which include meal choices that your kids are likely to enjoy. It can also help you to avoid those dining destinations that may result in a lot of whining and wasted food, because there is nothing much on the menu that your children are going to be willing to try. Go to:
http://allearsnet.com/menu/menus.htm
Tip #2 - Many of the 'All you can eat' buffet style restaraunts can be a wise choice with kids, since there are typically such a wide variety of food item choices available there. Chances are that even 'picky eaters' will be able to find something that they like. And there is no real harm done if they try something that looks interesting, and then decide they don't really like it--they can simply go back, get a new plate, and try something else. When ordering off of a regular menu, your options are often far more limited.