In the Animal Kingdom:
Pizzafari will serve you a salad with your pizza.
In the Studios:
Pizza Planet will serve you a salad with your pizza.
Fairfax Fare has a pretty standard baked-beans-and-coleslaw sides offering.
In Epcot:
Sunshine Seasons (the Land) will serve you stir-fried broccoli/mixed veg with your asian food, and they have some interesting entree salads.
In Magic Kingdom:
Cosmic Ray's serves their barbecue ribs and/or roasted chicken plates with 'seasonal vegetable' - it has been 'green bean season' for the past four or five years, apparently

Pinocchio's Village Haus serves their pizza with a side salad, and they also offer a couple of entree salads.
On top of this, every single location that sells burgers/sandwiches offers them with 'choice of apple slices or french fries' which could help eliminate fried-potato overload as well. I often order mine with apple slices and carry those off into the sunset for a snack later (they come in plastic packages).
It's not hard to eat a little better than standard burger-and-fries at QS locations in WDW, but we generally depend on our TS meals to load up on veggies.