Hi, Jeremy! Because you are going during the busy spring break period, I would recommend that you call ahead to make advanced dining reservations for the dining experiences you don't want to miss. Many of the most popular restaurants do book up in advance, and you may have to be flexible in terms of dining times and locations.
Some great locations to try, especially with kids, include Primetime 50s Cafe at Disney's Hollywood Studios; 'Ohana at the Polynesian Resort; Whispering Canyon at the Wilderness Lodge; and any of the character meals offered throughout the resort.
I would start by heading to
www.allears.net where you can click on the dining tab and find menus and recent pricing for all of the restaurants. This is a good place to get a rough idea of where you might like to eat, so when you call to make your dining reservations, you're all set.
Be flexible, and choose off peak hours to increase your chances of getting a reservation at a restaurant you want. Remember that you don't need reservations at all for the counter service meals, only the table service.
Good luck and have a wonderful vacation!