My favorite moderate-level resorts are both of the Port Orleans properties,
Riverside and
French Quarter. These are among the smallest of the moderate level resorts and for me, transportation has never been an issue. Both of these resorts have a relaxed vibe and getting around is as easy as pie. Boat service is available to and from Downtown Disney where you'll easily be able to board a Disney bus to your desired location.
Another great option to consider, if you wish to maximize your time, is
Disney's Fort Wilderness, also a moderate resort. Here, your family can relax with all the comforts of home in a rustic wilderness cabin. The best part is that you can hop aboard a water launch for direct service to the Magic Kingdom and the monorail which services Epcot as well as several Disney World Resort Hotels.
If you decide on one of the larger resorts, you may want to consider upgrading to a "preferred room" which will guarantee you a room assignment in a building or section closest to the main buildings, pools, food courts, and transportation. If you're looking to minimize walking time within the resort, springing for a "preferred room" will be well worth the money.
Happy vacation planning,
Amanda F.