Hi there, not sure about places in the parks but know that at the food court in Port Orleans you can definately get a milkshake as a dessert (well you could in May this year).
Its Sassagoula Floatworks in Port Orleans french quarter. They have the normal chicken nuggets and burgers but some other things also, copied menu below which may help.
16 Inch Pepperoni Pizza $15.49
16 Inch Meat Deluxe Pizza $17.99
16 Inch Veggie Deluxe Pizza $17.99
16 Inch Supreme Pizza $17.99
Choice of Toppings: Pepperoni, Onions, Sausage, Mushrooms, Ham, Peppers, or Jalapenos
Each Additional Topping $1.39
Tossed Salad $3.99
Meatball Sub $7.19
Veggie Sandwich $7.49
Pasta with Meatballs $8.09
Individual Pepperoni Pizza $6.09
Chicken Parmesan $8.79
Cheeseburger $6.09
Veggie Burger $6.29
Cheese Steak Sandwich $7.99
Double Cheeseburger $7.09
Grilled Chicken Sandwich $7.19
Chicken Breast Nuggets $7.69
Hot Dog $6.09
Chicken Caesar Salad $7.19
Taco Salad (beef or chicken) $7.39/$7.59
Ham or Turkey Sub (hot or cold) $6.79
Chicken Club Wrap $8.49
Muffaletta Sandwich $8.09
Chicken Quesadilla $8.39
Adult Meals served with fries or pasta salad
Adult Sandwiches served with chips or pasta salad
Souvenir Refillable Mug $12.49
Kids' Picks
For ages 9 and Under
All meals include choice of two side: grapes, carrot sticks or applesauce
and a beverage: 1% Mickey Milk, apple juice or small bottled water
Peanut Butter and Jelly $4.49
Chicken Nuggets $4.49
Grilled Cheese $4.49
Pasta with Marinara Sauce $4.49
Soft drinks and fries available upon request
--------------------------------------------------------------------------------
Ice Cream Cookie Sandwich $4.99
Beignets - six $4.29
Beignets - three $2.99
Assorted Cakes by the Slice $3.59
Freshly Baked Cookie $1.89
Cappuccino $3.19
Espresso $2.69
Hand-dipped Single Scoop Cone or Cup $2.69
Double Scoop Cone or Cup $3.69
Cheesecake with berries $3.89
Milkshakes $3.99
--------------------------------------------------------------------------------
DINNER ONLY
Pot Roast $9.79
Fried Chicken $9.49
Barbecue Rib Dinner $10.49
Chicken Jambalaya $9.49
Chicken and Rib Combo $13.99
Pork Chop $9.49
Kids' Picks
Macaroni and Cheese $4.49
On the dining plan you can use 2 dining plan credits to get 16 inch pizza, and you still get drink and dessert each.
The Beignets are to die for, well worth a try!