Hi Kim:
This question has many correct answers. I recommend Animal Kingdom Lodge, especially if you reserve a savanna-view room where your family can watch the animals walk by right outside your window. Upon entering the Animal Kingdom Lodge, your family will be mesmerized by the dramatic lobby expertly themed and filled with African artwork, artifacts, a fireplace (at Jambo House), and huge windows. The pools are great at Animal Kingdom Lodge. AKL Jambo House is home to the 11,000 square foot Uzima pool. The pool boasts a 67-foot slide as well as a tyke-friendly wading pool area. Not far away is a kids playground. AKL Kidani Village is home to the wonderful Samawati Springs pool and kids water playground. As you check in, request an activity guide from the front desk for a schedule of organized activities. Although subject to change, we found the following programs, among many others, available during our last stay: ceramics, cookie decorating, face painting, animal tracking, and African folktale storytelling. The Resort is home to a children's activity center, Simba's Cubhouse, for potty-trained children 3-12 years old.
I also recommend The Contemporary Resort, one of the original Walt Disney World Resorts. I still remember the wonder I felt as a six-year old staying at the Contemporary Resort and watching the monorail run right through the A-frame Tower and marveling at the lobby's 90-foot, floor-to-ceiling ceramic mural created by Disney Legend, Mary Blair. If you are looking at a Value Resort, I believe Pop Century and the new Art of Animation have the best themeing. Of course, my kids are just happy with
any Resort with a playground.
As for timing, you'll likely find that Disney World is slightly less crowded when schools are in session. I find October or early December (when the Parks and Resorts are decorated for the Holidays) are great times to visit.