Hi Matt,
Welcome to the Disney Parks Moms Panel! There is so much to do at the Walt Disney World Resort not only at the Theme Parks, but outside of them as well. Some of my family's favorite experiences have taken place at the Resort Hotels and Disney Springs so, here are a few suggestions for your half days:
Disney's Spirit of Aloha Dinner Show at Disney's Polynesian Village Resort:
The atmosphere is laid-back and relaxing, and the Hula and Fire Dancing performances are amazing. The menu is fantastic; I could just eat the pineapple-coconut bread all evening and be happy, however, the entire menu is delicious! Make sure to leave room for the pineapple bread pudding with caramel sauce for dessert!
The BOATHOUSE Restaurant in Disney Springs:
You can enjoy a wonderful meal by the water and enjoy the view of the Amphicars or go for a ride in one yourself!
Sanaa at Disney's Animal Kingdom Villas - Kidani Village:
The African/Indian inspired menu is great (the Indian-style Bread Service is a "must-eat") and just outside the Restaurant, there's a gorgeous view of the savanna where you can see giraffes, zebras, wildebeest, and a variety of other animals.
Cape May Cafe
at Disney's Beach Club Resort:
You'll get to meet classic Disney Characters while enjoying a delicious "all-you-care-to-enjoy" breakfast buffet. A morning with Mickey Mouse and Mickey waffles would be a great way to end your magical stay.
I hope these suggestions help in planning your visit!
~Susan